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||
line-height: 0;
|
||
padding: 4px;
|
||
}
|
||
.MathJax_Hover_Arrow:hover {
|
||
color: white !important;
|
||
border: 2px solid #ccc !important;
|
||
}
|
||
.MathJax_Hover_Arrow:hover span {
|
||
background-color: #ccc !important;
|
||
}
|
||
</style>
|
||
<style type="text/css">
|
||
#MathJax_About {
|
||
position: fixed;
|
||
left: 50%;
|
||
width: auto;
|
||
text-align: center;
|
||
border: 3px outset;
|
||
padding: 1em 2em;
|
||
background-color: #dddddd;
|
||
color: black;
|
||
cursor: default;
|
||
font-family: message-box;
|
||
font-size: 120%;
|
||
font-style: normal;
|
||
text-indent: 0;
|
||
text-transform: none;
|
||
line-height: normal;
|
||
letter-spacing: normal;
|
||
word-spacing: normal;
|
||
word-wrap: normal;
|
||
white-space: nowrap;
|
||
float: none;
|
||
z-index: 201;
|
||
border-radius: 15px;
|
||
-webkit-border-radius: 15px;
|
||
-moz-border-radius: 15px;
|
||
-khtml-border-radius: 15px;
|
||
box-shadow: 0px 10px 20px #808080;
|
||
-webkit-box-shadow: 0px 10px 20px #808080;
|
||
-moz-box-shadow: 0px 10px 20px #808080;
|
||
-khtml-box-shadow: 0px 10px 20px #808080;
|
||
filter: progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true');
|
||
}
|
||
#MathJax_About.MathJax_MousePost {
|
||
outline: none;
|
||
}
|
||
.MathJax_Menu {
|
||
position: absolute;
|
||
background-color: white;
|
||
color: black;
|
||
width: auto;
|
||
padding: 5px 0px;
|
||
border: 1px solid #cccccc;
|
||
margin: 0;
|
||
cursor: default;
|
||
font: menu;
|
||
text-align: left;
|
||
text-indent: 0;
|
||
text-transform: none;
|
||
line-height: normal;
|
||
letter-spacing: normal;
|
||
word-spacing: normal;
|
||
word-wrap: normal;
|
||
white-space: nowrap;
|
||
float: none;
|
||
z-index: 201;
|
||
border-radius: 5px;
|
||
-webkit-border-radius: 5px;
|
||
-moz-border-radius: 5px;
|
||
-khtml-border-radius: 5px;
|
||
box-shadow: 0px 10px 20px #808080;
|
||
-webkit-box-shadow: 0px 10px 20px #808080;
|
||
-moz-box-shadow: 0px 10px 20px #808080;
|
||
-khtml-box-shadow: 0px 10px 20px #808080;
|
||
filter: progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true');
|
||
}
|
||
.MathJax_MenuItem {
|
||
padding: 1px 2em;
|
||
background: transparent;
|
||
}
|
||
.MathJax_MenuArrow {
|
||
position: absolute;
|
||
right: 0.5em;
|
||
padding-top: 0.25em;
|
||
color: #666666;
|
||
font-size: 0.75em;
|
||
}
|
||
.MathJax_MenuActive .MathJax_MenuArrow {
|
||
color: white;
|
||
}
|
||
.MathJax_MenuArrow.RTL {
|
||
left: 0.5em;
|
||
right: auto;
|
||
}
|
||
.MathJax_MenuCheck {
|
||
position: absolute;
|
||
left: 0.7em;
|
||
}
|
||
.MathJax_MenuCheck.RTL {
|
||
right: 0.7em;
|
||
left: auto;
|
||
}
|
||
.MathJax_MenuRadioCheck {
|
||
position: absolute;
|
||
left: 0.7em;
|
||
}
|
||
.MathJax_MenuRadioCheck.RTL {
|
||
right: 0.7em;
|
||
left: auto;
|
||
}
|
||
.MathJax_MenuLabel {
|
||
padding: 1px 2em 3px 1.33em;
|
||
font-style: italic;
|
||
}
|
||
.MathJax_MenuRule {
|
||
border-top: 1px solid #dddddd;
|
||
margin: 4px 3px;
|
||
}
|
||
.MathJax_MenuDisabled {
|
||
color: GrayText;
|
||
}
|
||
.MathJax_MenuActive {
|
||
background-color: #606872;
|
||
color: white;
|
||
}
|
||
.MathJax_MenuDisabled:focus,
|
||
.MathJax_MenuLabel:focus {
|
||
background-color: #e8e8e8;
|
||
}
|
||
.MathJax_ContextMenu:focus {
|
||
outline: none;
|
||
}
|
||
.MathJax_ContextMenu .MathJax_MenuItem:focus {
|
||
outline: none;
|
||
}
|
||
#MathJax_AboutClose {
|
||
top: 0.2em;
|
||
right: 0.2em;
|
||
}
|
||
.MathJax_Menu .MathJax_MenuClose {
|
||
top: -10px;
|
||
left: -10px;
|
||
}
|
||
.MathJax_MenuClose {
|
||
position: absolute;
|
||
cursor: pointer;
|
||
display: inline-block;
|
||
border: 2px solid #aaa;
|
||
border-radius: 18px;
|
||
-webkit-border-radius: 18px;
|
||
-moz-border-radius: 18px;
|
||
-khtml-border-radius: 18px;
|
||
font-family: 'Courier New', Courier;
|
||
font-size: 24px;
|
||
color: #f0f0f0;
|
||
}
|
||
.MathJax_MenuClose span {
|
||
display: block;
|
||
background-color: #aaa;
|
||
border: 1.5px solid;
|
||
border-radius: 18px;
|
||
-webkit-border-radius: 18px;
|
||
-moz-border-radius: 18px;
|
||
-khtml-border-radius: 18px;
|
||
line-height: 0;
|
||
padding: 8px 0 6px;
|
||
}
|
||
.MathJax_MenuClose:hover {
|
||
color: white !important;
|
||
border: 2px solid #ccc !important;
|
||
}
|
||
.MathJax_MenuClose:hover span {
|
||
background-color: #ccc !important;
|
||
}
|
||
.MathJax_MenuClose:hover:focus {
|
||
outline: none;
|
||
}
|
||
</style>
|
||
<style type="text/css">
|
||
.MathJax_Preview .MJXf-math {
|
||
color: inherit !important;
|
||
}
|
||
</style>
|
||
<style type="text/css">
|
||
.MJX_Assistive_MathML {
|
||
position: absolute !important;
|
||
top: 0;
|
||
left: 0;
|
||
clip: rect(1px, 1px, 1px, 1px);
|
||
padding: 1px 0 0 0 !important;
|
||
border: 0 !important;
|
||
height: 1px !important;
|
||
width: 1px !important;
|
||
overflow: hidden !important;
|
||
display: block !important;
|
||
-webkit-touch-callout: none;
|
||
-webkit-user-select: none;
|
||
-khtml-user-select: none;
|
||
-moz-user-select: none;
|
||
-ms-user-select: none;
|
||
user-select: none;
|
||
}
|
||
.MJX_Assistive_MathML.MJX_Assistive_MathML_Block {
|
||
width: 100% !important;
|
||
}
|
||
</style>
|
||
<style type="text/css">
|
||
#MathJax_Zoom {
|
||
position: absolute;
|
||
background-color: #f0f0f0;
|
||
overflow: auto;
|
||
display: block;
|
||
z-index: 301;
|
||
padding: 0.5em;
|
||
border: 1px solid black;
|
||
margin: 0;
|
||
font-weight: normal;
|
||
font-style: normal;
|
||
text-align: left;
|
||
text-indent: 0;
|
||
text-transform: none;
|
||
line-height: normal;
|
||
letter-spacing: normal;
|
||
word-spacing: normal;
|
||
word-wrap: normal;
|
||
white-space: nowrap;
|
||
float: none;
|
||
-webkit-box-sizing: content-box;
|
||
-moz-box-sizing: content-box;
|
||
box-sizing: content-box;
|
||
box-shadow: 5px 5px 15px #aaaaaa;
|
||
-webkit-box-shadow: 5px 5px 15px #aaaaaa;
|
||
-moz-box-shadow: 5px 5px 15px #aaaaaa;
|
||
-khtml-box-shadow: 5px 5px 15px #aaaaaa;
|
||
filter: progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true');
|
||
}
|
||
#MathJax_ZoomOverlay {
|
||
position: absolute;
|
||
left: 0;
|
||
top: 0;
|
||
z-index: 300;
|
||
display: inline-block;
|
||
width: 100%;
|
||
height: 100%;
|
||
border: 0;
|
||
padding: 0;
|
||
margin: 0;
|
||
background-color: white;
|
||
opacity: 0;
|
||
filter: alpha(opacity=0);
|
||
}
|
||
#MathJax_ZoomFrame {
|
||
position: relative;
|
||
display: inline-block;
|
||
height: 0;
|
||
width: 0;
|
||
}
|
||
#MathJax_ZoomEventTrap {
|
||
position: absolute;
|
||
left: 0;
|
||
top: 0;
|
||
z-index: 302;
|
||
display: inline-block;
|
||
border: 0;
|
||
padding: 0;
|
||
margin: 0;
|
||
background-color: white;
|
||
opacity: 0;
|
||
filter: alpha(opacity=0);
|
||
}
|
||
</style>
|
||
<style type="text/css">
|
||
.MathJax_Preview {
|
||
color: #888;
|
||
display: contents;
|
||
}
|
||
#MathJax_Message {
|
||
position: fixed;
|
||
left: 1px;
|
||
bottom: 2px;
|
||
background-color: #e6e6e6;
|
||
border: 1px solid #959595;
|
||
margin: 0px;
|
||
padding: 2px 8px;
|
||
z-index: 102;
|
||
color: black;
|
||
font-size: 80%;
|
||
width: auto;
|
||
white-space: nowrap;
|
||
}
|
||
#MathJax_MSIE_Frame {
|
||
position: absolute;
|
||
top: 0;
|
||
left: 0;
|
||
width: 0px;
|
||
z-index: 101;
|
||
border: 0px;
|
||
margin: 0px;
|
||
padding: 0px;
|
||
}
|
||
.MathJax_Error {
|
||
color: #cc0000;
|
||
font-style: italic;
|
||
}
|
||
</style>
|
||
<script
|
||
type="text/javascript"
|
||
src="https://codeforces.com/mathjax.codeforces.org/jax/output/HTML-CSS/fonts/TeX/fontdata.js?V=2.7.9"
|
||
></script>
|
||
<style type="text/css">
|
||
.MJXp-script {
|
||
font-size: 0.8em;
|
||
}
|
||
.MJXp-right {
|
||
-webkit-transform-origin: right;
|
||
-moz-transform-origin: right;
|
||
-ms-transform-origin: right;
|
||
-o-transform-origin: right;
|
||
transform-origin: right;
|
||
}
|
||
.MJXp-bold {
|
||
font-weight: bold;
|
||
}
|
||
.MJXp-italic {
|
||
font-style: italic;
|
||
}
|
||
.MJXp-scr {
|
||
font-family:
|
||
MathJax_Script, 'Times New Roman', Times, STIXGeneral, serif;
|
||
}
|
||
.MJXp-frak {
|
||
font-family:
|
||
MathJax_Fraktur, 'Times New Roman', Times, STIXGeneral, serif;
|
||
}
|
||
.MJXp-sf {
|
||
font-family:
|
||
MathJax_SansSerif, 'Times New Roman', Times, STIXGeneral, serif;
|
||
}
|
||
.MJXp-cal {
|
||
font-family:
|
||
MathJax_Caligraphic, 'Times New Roman', Times, STIXGeneral, serif;
|
||
}
|
||
.MJXp-mono {
|
||
font-family:
|
||
MathJax_Typewriter, 'Times New Roman', Times, STIXGeneral, serif;
|
||
}
|
||
.MJXp-largeop {
|
||
font-size: 150%;
|
||
}
|
||
.MJXp-largeop.MJXp-int {
|
||
vertical-align: -0.2em;
|
||
}
|
||
.MJXp-math {
|
||
display: inline-block;
|
||
line-height: 1.2;
|
||
text-indent: 0;
|
||
font-family: 'Times New Roman', Times, STIXGeneral, serif;
|
||
white-space: nowrap;
|
||
border-collapse: collapse;
|
||
}
|
||
.MJXp-display {
|
||
display: block;
|
||
text-align: center;
|
||
margin: 1em 0;
|
||
}
|
||
.MJXp-math span {
|
||
display: inline-block;
|
||
}
|
||
.MJXp-box {
|
||
display: block !important;
|
||
text-align: center;
|
||
}
|
||
.MJXp-box:after {
|
||
content: ' ';
|
||
}
|
||
.MJXp-rule {
|
||
display: block !important;
|
||
margin-top: 0.1em;
|
||
}
|
||
.MJXp-char {
|
||
display: block !important;
|
||
}
|
||
.MJXp-mo {
|
||
margin: 0 0.15em;
|
||
}
|
||
.MJXp-mfrac {
|
||
margin: 0 0.125em;
|
||
vertical-align: 0.25em;
|
||
}
|
||
.MJXp-denom {
|
||
display: inline-table !important;
|
||
width: 100%;
|
||
}
|
||
.MJXp-denom > * {
|
||
display: table-row !important;
|
||
}
|
||
.MJXp-surd {
|
||
vertical-align: top;
|
||
}
|
||
.MJXp-surd > * {
|
||
display: block !important;
|
||
}
|
||
.MJXp-script-box > * {
|
||
display: table !important;
|
||
height: 50%;
|
||
}
|
||
.MJXp-script-box > * > * {
|
||
display: table-cell !important;
|
||
vertical-align: top;
|
||
}
|
||
.MJXp-script-box > *:last-child > * {
|
||
vertical-align: bottom;
|
||
}
|
||
.MJXp-script-box > * > * > * {
|
||
display: block !important;
|
||
}
|
||
.MJXp-mphantom {
|
||
visibility: hidden;
|
||
}
|
||
.MJXp-munderover,
|
||
.MJXp-munder {
|
||
display: inline-table !important;
|
||
}
|
||
.MJXp-over {
|
||
display: inline-block !important;
|
||
text-align: center;
|
||
}
|
||
.MJXp-over > * {
|
||
display: block !important;
|
||
}
|
||
.MJXp-munderover > *,
|
||
.MJXp-munder > * {
|
||
display: table-row !important;
|
||
}
|
||
.MJXp-mtable {
|
||
vertical-align: 0.25em;
|
||
margin: 0 0.125em;
|
||
}
|
||
.MJXp-mtable > * {
|
||
display: inline-table !important;
|
||
vertical-align: middle;
|
||
}
|
||
.MJXp-mtr {
|
||
display: table-row !important;
|
||
}
|
||
.MJXp-mtd {
|
||
display: table-cell !important;
|
||
text-align: center;
|
||
padding: 0.5em 0 0 0.5em;
|
||
}
|
||
.MJXp-mtr > .MJXp-mtd:first-child {
|
||
padding-left: 0;
|
||
}
|
||
.MJXp-mtr:first-child > .MJXp-mtd {
|
||
padding-top: 0;
|
||
}
|
||
.MJXp-mlabeledtr {
|
||
display: table-row !important;
|
||
}
|
||
.MJXp-mlabeledtr > .MJXp-mtd:first-child {
|
||
padding-left: 0;
|
||
}
|
||
.MJXp-mlabeledtr:first-child > .MJXp-mtd {
|
||
padding-top: 0;
|
||
}
|
||
.MJXp-merror {
|
||
background-color: #ffff88;
|
||
color: #cc0000;
|
||
border: 1px solid #cc0000;
|
||
padding: 1px 3px;
|
||
font-style: normal;
|
||
font-size: 90%;
|
||
}
|
||
.MJXp-scale0 {
|
||
-webkit-transform: scaleX(0);
|
||
-moz-transform: scaleX(0);
|
||
-ms-transform: scaleX(0);
|
||
-o-transform: scaleX(0);
|
||
transform: scaleX(0);
|
||
}
|
||
.MJXp-scale1 {
|
||
-webkit-transform: scaleX(0.1);
|
||
-moz-transform: scaleX(0.1);
|
||
-ms-transform: scaleX(0.1);
|
||
-o-transform: scaleX(0.1);
|
||
transform: scaleX(0.1);
|
||
}
|
||
.MJXp-scale2 {
|
||
-webkit-transform: scaleX(0.2);
|
||
-moz-transform: scaleX(0.2);
|
||
-ms-transform: scaleX(0.2);
|
||
-o-transform: scaleX(0.2);
|
||
transform: scaleX(0.2);
|
||
}
|
||
.MJXp-scale3 {
|
||
-webkit-transform: scaleX(0.3);
|
||
-moz-transform: scaleX(0.3);
|
||
-ms-transform: scaleX(0.3);
|
||
-o-transform: scaleX(0.3);
|
||
transform: scaleX(0.3);
|
||
}
|
||
.MJXp-scale4 {
|
||
-webkit-transform: scaleX(0.4);
|
||
-moz-transform: scaleX(0.4);
|
||
-ms-transform: scaleX(0.4);
|
||
-o-transform: scaleX(0.4);
|
||
transform: scaleX(0.4);
|
||
}
|
||
.MJXp-scale5 {
|
||
-webkit-transform: scaleX(0.5);
|
||
-moz-transform: scaleX(0.5);
|
||
-ms-transform: scaleX(0.5);
|
||
-o-transform: scaleX(0.5);
|
||
transform: scaleX(0.5);
|
||
}
|
||
.MJXp-scale6 {
|
||
-webkit-transform: scaleX(0.6);
|
||
-moz-transform: scaleX(0.6);
|
||
-ms-transform: scaleX(0.6);
|
||
-o-transform: scaleX(0.6);
|
||
transform: scaleX(0.6);
|
||
}
|
||
.MJXp-scale7 {
|
||
-webkit-transform: scaleX(0.7);
|
||
-moz-transform: scaleX(0.7);
|
||
-ms-transform: scaleX(0.7);
|
||
-o-transform: scaleX(0.7);
|
||
transform: scaleX(0.7);
|
||
}
|
||
.MJXp-scale8 {
|
||
-webkit-transform: scaleX(0.8);
|
||
-moz-transform: scaleX(0.8);
|
||
-ms-transform: scaleX(0.8);
|
||
-o-transform: scaleX(0.8);
|
||
transform: scaleX(0.8);
|
||
}
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|
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|
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Educational Codeforces Round 111 (Rated for Div. 2)
|
||
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
||
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|
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|
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|
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|
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|
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|
||
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|
||
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
||
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|
||
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|
||
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|
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|
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|
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|
||
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|
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.join('\n')
|
||
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|
||
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|
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|
||
|
||
<div
|
||
class="problemindexholder"
|
||
problemindex="A"
|
||
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|
||
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|
||
<div
|
||
style="
|
||
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|
||
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|
||
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|
||
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|
||
"
|
||
class="alert alert-info diff-notifier"
|
||
>
|
||
<div>
|
||
The problem statement has recently been changed.
|
||
<a class="view-changes" href="#">View the changes.</a>
|
||
</div>
|
||
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|
||
class="diff-notifier-close"
|
||
style="
|
||
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|
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|
||
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|
||
cursor: pointer;
|
||
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|
||
"
|
||
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|
||
>
|
||
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|
||
<div class="ttypography">
|
||
<div class="problem-statement">
|
||
<div class="header">
|
||
<div class="title">A. Find The Array</div>
|
||
<div class="time-limit">
|
||
<div class="property-title">time limit per test</div>
|
||
1 second
|
||
</div>
|
||
<div class="memory-limit">
|
||
<div class="property-title">memory limit per test</div>
|
||
256 megabytes
|
||
</div>
|
||
<div class="input-file input-standard">
|
||
<div class="property-title">input</div>
|
||
standard input
|
||
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|
||
<div class="output-file output-standard">
|
||
<div class="property-title">output</div>
|
||
standard output
|
||
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|
||
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|
||
<div>
|
||
<p>
|
||
Let's call an array
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
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|
||
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|
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|
||
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|
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|
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|
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|
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a
|
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|
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|
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|
||
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|
||
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|
||
>n</span
|
||
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|
||
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|
||
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|
||
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|
||
n
|
||
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|
||
positive (greater than
|
||
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|
||
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|
||
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|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-3">
|
||
0
|
||
</script>
|
||
) integers
|
||
<span class="tex-font-style-it">beautiful</span> if the
|
||
following condition is held for every
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-7"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-8"
|
||
>i</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-4">
|
||
i
|
||
</script>
|
||
from
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-9"
|
||
><span class="MJXp-mn" id="MJXp-Span-10"
|
||
>1</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-5">
|
||
1
|
||
</script>
|
||
to
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-11"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-12"
|
||
>n</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-6">
|
||
n
|
||
</script>
|
||
: either
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-13"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-14"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-15"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-16"
|
||
style="vertical-align: -0.4em"
|
||
>i</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-17"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>=</span
|
||
><span class="MJXp-mn" id="MJXp-Span-18"
|
||
>1</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-7">
|
||
a_i = 1
|
||
</script>
|
||
, or at least one of the numbers
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-19"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-20"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-21"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-22"
|
||
style="vertical-align: -0.4em"
|
||
>i</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-23"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>−</span
|
||
><span class="MJXp-mn" id="MJXp-Span-24"
|
||
>1</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-8">
|
||
a_i - 1
|
||
</script>
|
||
and
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-25"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-26"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-27"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-28"
|
||
style="vertical-align: -0.4em"
|
||
>i</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-29"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>−</span
|
||
><span class="MJXp-mn" id="MJXp-Span-30"
|
||
>2</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-9">
|
||
a_i - 2
|
||
</script>
|
||
exists in the array as well.
|
||
</p>
|
||
<p>For example:</p>
|
||
<ul>
|
||
<li>
|
||
the array
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-31"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-32"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>[</span
|
||
><span class="MJXp-mn" id="MJXp-Span-33">5</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-34"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-35">3</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-36"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-37">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-38"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>]</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-10">
|
||
[5, 3, 1]
|
||
</script>
|
||
is beautiful: for
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-39"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-40"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-41"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-42"
|
||
style="vertical-align: -0.4em"
|
||
>1</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-11">
|
||
a_1
|
||
</script>
|
||
, the number
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-43"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-44"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-45"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-46"
|
||
style="vertical-align: -0.4em"
|
||
>1</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-47"
|
||
style="
|
||
margin-left: 0.267em;
|
||
margin-right: 0.267em;
|
||
"
|
||
>−</span
|
||
><span class="MJXp-mn" id="MJXp-Span-48">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-49"
|
||
style="
|
||
margin-left: 0.333em;
|
||
margin-right: 0.333em;
|
||
"
|
||
>=</span
|
||
><span class="MJXp-mn" id="MJXp-Span-50"
|
||
>3</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-12">
|
||
a_1 - 2 = 3
|
||
</script>
|
||
exists in the array; for
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-51"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-52"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-53"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-54"
|
||
style="vertical-align: -0.4em"
|
||
>2</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-13">
|
||
a_2
|
||
</script>
|
||
, the number
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-55"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-56"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-57"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-58"
|
||
style="vertical-align: -0.4em"
|
||
>2</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-59"
|
||
style="
|
||
margin-left: 0.267em;
|
||
margin-right: 0.267em;
|
||
"
|
||
>−</span
|
||
><span class="MJXp-mn" id="MJXp-Span-60">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-61"
|
||
style="
|
||
margin-left: 0.333em;
|
||
margin-right: 0.333em;
|
||
"
|
||
>=</span
|
||
><span class="MJXp-mn" id="MJXp-Span-62"
|
||
>1</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-14">
|
||
a_2 - 2 = 1
|
||
</script>
|
||
exists in the array; for
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-63"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-64"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-65"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-66"
|
||
style="vertical-align: -0.4em"
|
||
>3</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-15">
|
||
a_3
|
||
</script>
|
||
, the condition
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-67"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-68"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-69"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-70"
|
||
style="vertical-align: -0.4em"
|
||
>3</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-71"
|
||
style="
|
||
margin-left: 0.333em;
|
||
margin-right: 0.333em;
|
||
"
|
||
>=</span
|
||
><span class="MJXp-mn" id="MJXp-Span-72"
|
||
>1</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-16">
|
||
a_3 = 1
|
||
</script>
|
||
holds;
|
||
</li>
|
||
<li>
|
||
the array
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-73"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-74"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>[</span
|
||
><span class="MJXp-mn" id="MJXp-Span-75">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-76"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-77">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-78"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-79">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-80"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-81">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-82"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-83">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-84"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>]</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-17">
|
||
[1, 2, 2, 2, 2]
|
||
</script>
|
||
is beautiful: for
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-85"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-86"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-87"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-88"
|
||
style="vertical-align: -0.4em"
|
||
>1</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-18">
|
||
a_1
|
||
</script>
|
||
, the condition
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-89"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-90"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-91"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-92"
|
||
style="vertical-align: -0.4em"
|
||
>1</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-93"
|
||
style="
|
||
margin-left: 0.333em;
|
||
margin-right: 0.333em;
|
||
"
|
||
>=</span
|
||
><span class="MJXp-mn" id="MJXp-Span-94"
|
||
>1</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-19">
|
||
a_1 = 1
|
||
</script>
|
||
holds; for every other number
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-95"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-96"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-97"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-98"
|
||
style="vertical-align: -0.4em"
|
||
>i</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-20">
|
||
a_i
|
||
</script>
|
||
, the number
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-99"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-100"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-101"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-102"
|
||
style="vertical-align: -0.4em"
|
||
>i</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-103"
|
||
style="
|
||
margin-left: 0.267em;
|
||
margin-right: 0.267em;
|
||
"
|
||
>−</span
|
||
><span class="MJXp-mn" id="MJXp-Span-104">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-105"
|
||
style="
|
||
margin-left: 0.333em;
|
||
margin-right: 0.333em;
|
||
"
|
||
>=</span
|
||
><span class="MJXp-mn" id="MJXp-Span-106"
|
||
>1</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-21">
|
||
a_i - 1 = 1
|
||
</script>
|
||
exists in the array;
|
||
</li>
|
||
<li>
|
||
the array
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-107"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-108"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>[</span
|
||
><span class="MJXp-mn" id="MJXp-Span-109">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-110"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-111">4</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-112"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>]</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-22">
|
||
[1, 4]
|
||
</script>
|
||
is not beautiful: for
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-113"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-114"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-115"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-116"
|
||
style="vertical-align: -0.4em"
|
||
>2</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-23">
|
||
a_2
|
||
</script>
|
||
, neither
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-117"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-118"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-119"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-120"
|
||
style="vertical-align: -0.4em"
|
||
>2</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-121"
|
||
style="
|
||
margin-left: 0.267em;
|
||
margin-right: 0.267em;
|
||
"
|
||
>−</span
|
||
><span class="MJXp-mn" id="MJXp-Span-122">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-123"
|
||
style="
|
||
margin-left: 0.333em;
|
||
margin-right: 0.333em;
|
||
"
|
||
>=</span
|
||
><span class="MJXp-mn" id="MJXp-Span-124"
|
||
>2</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-24">
|
||
a_2 - 2 = 2
|
||
</script>
|
||
nor
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-125"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-126"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-127"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-128"
|
||
style="vertical-align: -0.4em"
|
||
>2</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-129"
|
||
style="
|
||
margin-left: 0.267em;
|
||
margin-right: 0.267em;
|
||
"
|
||
>−</span
|
||
><span class="MJXp-mn" id="MJXp-Span-130">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-131"
|
||
style="
|
||
margin-left: 0.333em;
|
||
margin-right: 0.333em;
|
||
"
|
||
>=</span
|
||
><span class="MJXp-mn" id="MJXp-Span-132"
|
||
>3</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-25">
|
||
a_2 - 1 = 3
|
||
</script>
|
||
exists in the array, and
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-133"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-134"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-135"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-136"
|
||
style="vertical-align: -0.4em"
|
||
>2</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-137"
|
||
style="
|
||
margin-left: 0.333em;
|
||
margin-right: 0.333em;
|
||
"
|
||
>≠</span
|
||
><span class="MJXp-mn" id="MJXp-Span-138"
|
||
>1</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-26">
|
||
a_2 \ne 1
|
||
</script>
|
||
;
|
||
</li>
|
||
<li>
|
||
the array
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-139"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-140"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>[</span
|
||
><span class="MJXp-mn" id="MJXp-Span-141">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-142"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>]</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-27">
|
||
[2]
|
||
</script>
|
||
is not beautiful: for
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-143"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-144"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-145"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-146"
|
||
style="vertical-align: -0.4em"
|
||
>1</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-28">
|
||
a_1
|
||
</script>
|
||
, neither
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-147"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-148"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-149"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-150"
|
||
style="vertical-align: -0.4em"
|
||
>1</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-151"
|
||
style="
|
||
margin-left: 0.267em;
|
||
margin-right: 0.267em;
|
||
"
|
||
>−</span
|
||
><span class="MJXp-mn" id="MJXp-Span-152">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-153"
|
||
style="
|
||
margin-left: 0.333em;
|
||
margin-right: 0.333em;
|
||
"
|
||
>=</span
|
||
><span class="MJXp-mn" id="MJXp-Span-154"
|
||
>1</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-29">
|
||
a_1 - 1 = 1
|
||
</script>
|
||
nor
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-155"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-156"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-157"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-158"
|
||
style="vertical-align: -0.4em"
|
||
>1</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-159"
|
||
style="
|
||
margin-left: 0.267em;
|
||
margin-right: 0.267em;
|
||
"
|
||
>−</span
|
||
><span class="MJXp-mn" id="MJXp-Span-160">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-161"
|
||
style="
|
||
margin-left: 0.333em;
|
||
margin-right: 0.333em;
|
||
"
|
||
>=</span
|
||
><span class="MJXp-mn" id="MJXp-Span-162"
|
||
>0</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-30">
|
||
a_1 - 2 = 0
|
||
</script>
|
||
exists in the array, and
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-163"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-164"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-165"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-166"
|
||
style="vertical-align: -0.4em"
|
||
>1</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-167"
|
||
style="
|
||
margin-left: 0.333em;
|
||
margin-right: 0.333em;
|
||
"
|
||
>≠</span
|
||
><span class="MJXp-mn" id="MJXp-Span-168"
|
||
>1</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-31">
|
||
a_1 \ne 1
|
||
</script>
|
||
;
|
||
</li>
|
||
<li>
|
||
the array
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-169"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-170"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>[</span
|
||
><span class="MJXp-mn" id="MJXp-Span-171">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-172"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-173">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-174"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-175">3</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-176"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>]</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-32">
|
||
[2, 1, 3]
|
||
</script>
|
||
is beautiful: for
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-177"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-178"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-179"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-180"
|
||
style="vertical-align: -0.4em"
|
||
>1</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-33">
|
||
a_1
|
||
</script>
|
||
, the number
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-181"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-182"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-183"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-184"
|
||
style="vertical-align: -0.4em"
|
||
>1</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-185"
|
||
style="
|
||
margin-left: 0.267em;
|
||
margin-right: 0.267em;
|
||
"
|
||
>−</span
|
||
><span class="MJXp-mn" id="MJXp-Span-186">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-187"
|
||
style="
|
||
margin-left: 0.333em;
|
||
margin-right: 0.333em;
|
||
"
|
||
>=</span
|
||
><span class="MJXp-mn" id="MJXp-Span-188"
|
||
>1</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-34">
|
||
a_1 - 1 = 1
|
||
</script>
|
||
exists in the array; for
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-189"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-190"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-191"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-192"
|
||
style="vertical-align: -0.4em"
|
||
>2</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-35">
|
||
a_2
|
||
</script>
|
||
, the condition
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-193"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-194"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-195"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-196"
|
||
style="vertical-align: -0.4em"
|
||
>2</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-197"
|
||
style="
|
||
margin-left: 0.333em;
|
||
margin-right: 0.333em;
|
||
"
|
||
>=</span
|
||
><span class="MJXp-mn" id="MJXp-Span-198"
|
||
>1</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-36">
|
||
a_2 = 1
|
||
</script>
|
||
holds; for
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-199"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-200"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-201"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-202"
|
||
style="vertical-align: -0.4em"
|
||
>3</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-37">
|
||
a_3
|
||
</script>
|
||
, the number
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-203"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-204"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-205"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-206"
|
||
style="vertical-align: -0.4em"
|
||
>3</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-207"
|
||
style="
|
||
margin-left: 0.267em;
|
||
margin-right: 0.267em;
|
||
"
|
||
>−</span
|
||
><span class="MJXp-mn" id="MJXp-Span-208">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-209"
|
||
style="
|
||
margin-left: 0.333em;
|
||
margin-right: 0.333em;
|
||
"
|
||
>=</span
|
||
><span class="MJXp-mn" id="MJXp-Span-210"
|
||
>1</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-38">
|
||
a_3 - 2 = 1
|
||
</script>
|
||
exists in the array.
|
||
</li>
|
||
</ul>
|
||
<p>
|
||
You are given a positive integer
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-211"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-212"
|
||
>s</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-39">
|
||
s
|
||
</script>
|
||
. Find the minimum possible size of a beautiful array with
|
||
the sum of elements equal to
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-213"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-214"
|
||
>s</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-40">
|
||
s
|
||
</script>
|
||
.
|
||
</p>
|
||
</div>
|
||
<div class="input-specification">
|
||
<div class="section-title">Input</div>
|
||
<p>
|
||
The first line contains one integer
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-215"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-216"
|
||
>t</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-41">
|
||
t
|
||
</script>
|
||
(<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-217"
|
||
><span class="MJXp-mn" id="MJXp-Span-218">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-219"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-220"
|
||
>t</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-221"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mn" id="MJXp-Span-222"
|
||
>5000</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-42">
|
||
1 \le t \le 5000
|
||
</script>
|
||
) — the number of test cases.
|
||
</p>
|
||
<p>
|
||
Then
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-223"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-224"
|
||
>t</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-43">
|
||
t
|
||
</script>
|
||
lines follow, the
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-225"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-226"
|
||
>i</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-44">
|
||
i
|
||
</script>
|
||
-th line contains one integer
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-227"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-228"
|
||
>s</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-45">
|
||
s
|
||
</script>
|
||
(<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-229"
|
||
><span class="MJXp-mn" id="MJXp-Span-230">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-231"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-232"
|
||
>s</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-233"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mn" id="MJXp-Span-234"
|
||
>5000</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-46">
|
||
1 \le s \le 5000
|
||
</script>
|
||
) for the
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-235"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-236"
|
||
>i</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-47">
|
||
i
|
||
</script>
|
||
-th test case.
|
||
</p>
|
||
</div>
|
||
<div class="output-specification">
|
||
<div class="section-title">Output</div>
|
||
<p>
|
||
Print
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-237"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-238"
|
||
>t</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-48">
|
||
t
|
||
</script>
|
||
integers, the
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-239"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-240"
|
||
>i</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-49">
|
||
i
|
||
</script>
|
||
-th integer should be the answer for the
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-241"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-242"
|
||
>i</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-50">
|
||
i
|
||
</script>
|
||
-th testcase: the minimum possible size of a beautiful
|
||
array with the sum of elements equal to
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-243"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-244"
|
||
>s</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-51">
|
||
s
|
||
</script>
|
||
.
|
||
</p>
|
||
</div>
|
||
<div class="sample-tests">
|
||
<div class="section-title">Example</div>
|
||
<div class="sample-test">
|
||
<div class="input">
|
||
<div class="title">
|
||
Input
|
||
<div
|
||
title="Copy"
|
||
data-clipboard-target="#id0011335133290051413"
|
||
id="id007175500850450626"
|
||
class="input-output-copier"
|
||
>
|
||
Copy
|
||
</div>
|
||
</div>
|
||
<pre id="id0011335133290051413">
|
||
4
|
||
1
|
||
8
|
||
7
|
||
42
|
||
</pre
|
||
>
|
||
</div>
|
||
<div class="output">
|
||
<div class="title">
|
||
Output
|
||
<div
|
||
title="Copy"
|
||
data-clipboard-target="#id005021691657849819"
|
||
id="id004270717779247326"
|
||
class="input-output-copier"
|
||
>
|
||
Copy
|
||
</div>
|
||
</div>
|
||
<pre id="id005021691657849819">
|
||
1
|
||
3
|
||
3
|
||
7
|
||
</pre
|
||
>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<div class="note">
|
||
<div class="section-title">Note</div>
|
||
<p>Consider the example test:</p>
|
||
<ol>
|
||
<li>
|
||
in the first test case, the array
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-245"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-246"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>[</span
|
||
><span class="MJXp-mn" id="MJXp-Span-247">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-248"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>]</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-52">
|
||
[1]
|
||
</script>
|
||
meets all conditions;
|
||
</li>
|
||
<li>
|
||
in the second test case, the array
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-249"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-250"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>[</span
|
||
><span class="MJXp-mn" id="MJXp-Span-251">3</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-252"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-253">4</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-254"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-255">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-256"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>]</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-53">
|
||
[3, 4, 1]
|
||
</script>
|
||
meets all conditions;
|
||
</li>
|
||
<li>
|
||
in the third test case, the array
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-257"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-258"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>[</span
|
||
><span class="MJXp-mn" id="MJXp-Span-259">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-260"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-261">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-262"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-263">4</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-264"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>]</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-54">
|
||
[1, 2, 4]
|
||
</script>
|
||
meets all conditions;
|
||
</li>
|
||
<li>
|
||
in the fourth test case, the array
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-265"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-266"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>[</span
|
||
><span class="MJXp-mn" id="MJXp-Span-267">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-268"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-269">4</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-270"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-271">6</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-272"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-273">8</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-274"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-275">10</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-276"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-277">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-278"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-279">11</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-280"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>]</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-55">
|
||
[1, 4, 6, 8, 10, 2, 11]
|
||
</script>
|
||
meets all conditions.
|
||
</li>
|
||
</ol>
|
||
</div>
|
||
</div>
|
||
<p></p>
|
||
</div>
|
||
</div>
|
||
|
||
<script>
|
||
$(function () {
|
||
Codeforces.addMathJaxListener(function () {
|
||
let $problem = $('div[problemindex=A]')
|
||
let uuid = $problem.attr('data-uuid')
|
||
let statementText = convertStatementToText(
|
||
$problem.find('.ttypography').get(0)
|
||
)
|
||
|
||
let previousStatementText = Codeforces.getFromStorage(uuid)
|
||
if (previousStatementText) {
|
||
if (previousStatementText !== statementText) {
|
||
$problem.find('.diff-notifier').show()
|
||
|
||
$problem.find('.diff-notifier-close').click(function () {
|
||
Codeforces.putToStorageTtl(
|
||
uuid,
|
||
statementText,
|
||
6 * 60 * 60
|
||
)
|
||
$problem.find('.diff-notifier').hide()
|
||
})
|
||
|
||
$problem.find('a.view-changes').click(function () {
|
||
$.post(
|
||
'/data/diff',
|
||
{
|
||
action: 'getDiff',
|
||
a: previousStatementText,
|
||
b: statementText
|
||
},
|
||
function (result) {
|
||
if (result['success'] === 'true') {
|
||
Codeforces.facebox(
|
||
'.diff-popup',
|
||
'//codeforces.org/s/15523'
|
||
)
|
||
$('#facebox .diff-popup').html(result['diff'])
|
||
}
|
||
},
|
||
'json'
|
||
)
|
||
})
|
||
}
|
||
} else {
|
||
Codeforces.putToStorageTtl(uuid, statementText, 6 * 60 * 60)
|
||
}
|
||
})
|
||
})
|
||
</script>
|
||
<script type="text/javascript">
|
||
$(document).ready(function () {
|
||
window.changedTests = new Set()
|
||
|
||
const inputFileDiv = $('div.input-file')
|
||
const inputFile = inputFileDiv.text()
|
||
const outputFileDiv = $('div.output-file')
|
||
const outputFile = outputFileDiv.text()
|
||
|
||
if (
|
||
!endsWith(inputFile, 'standard input') &&
|
||
!endsWith(inputFile, 'standard input')
|
||
) {
|
||
inputFileDiv.attr('style', 'font-weight: bold')
|
||
}
|
||
|
||
if (
|
||
!endsWith(outputFile, 'standard output') &&
|
||
!endsWith(outputFile, 'standard output')
|
||
) {
|
||
outputFileDiv.attr('style', 'font-weight: bold')
|
||
}
|
||
|
||
const titleDiv = $('div.header div.title')
|
||
|
||
String.prototype.replaceAll = function (search, replace) {
|
||
return this.split(search).join(replace)
|
||
}
|
||
|
||
$('.sample-test .title').each(function () {
|
||
const preId = ('id' + Math.random()).replaceAll('.', '0')
|
||
const cpyId = ('id' + Math.random()).replaceAll('.', '0')
|
||
|
||
$(this).parent().find('pre').attr('id', preId)
|
||
const $copy = $(
|
||
"<div title='Copy' data-clipboard-target='#" +
|
||
preId +
|
||
"' id='" +
|
||
cpyId +
|
||
"' class='input-output-copier'>Copy</div>"
|
||
)
|
||
$(this).append($copy)
|
||
|
||
const clipboard = new Clipboard('#' + cpyId, {
|
||
text: function (trigger) {
|
||
const pre = document.querySelector('#' + preId)
|
||
const lines = pre.querySelectorAll('.test-example-line')
|
||
return Codeforces.filterClipboardText(
|
||
pre.innerText,
|
||
lines.length
|
||
)
|
||
}
|
||
})
|
||
|
||
const isInput = $(this).parent().hasClass('input')
|
||
|
||
clipboard.on('success', function (e) {
|
||
if (isInput) {
|
||
Codeforces.showMessage(
|
||
'The example input has been copied into the clipboard'
|
||
)
|
||
} else {
|
||
Codeforces.showMessage(
|
||
'The example output has been copied into the clipboard'
|
||
)
|
||
}
|
||
e.clearSelection()
|
||
})
|
||
})
|
||
|
||
$('.test-form-item input').change(function () {
|
||
addPendingSubmissionMessage(
|
||
$($(this).closest('form')),
|
||
'You changed the answer, do not forget to submit it if you want to save the changes'
|
||
)
|
||
const index = $(this)
|
||
.closest('.problemindexholder')
|
||
.attr('problemindex')
|
||
let test = ''
|
||
$(this)
|
||
.closest('form input')
|
||
.each(function () {
|
||
const test_ = $(this).attr('name')
|
||
if (test_ && test_.substring(0, 4) === 'test') {
|
||
test = test_
|
||
}
|
||
})
|
||
if (index.length > 0 && test.length > 0) {
|
||
const indexTest = index + '::' + test
|
||
window.changedTests.add(indexTest)
|
||
}
|
||
})
|
||
|
||
$(window).on('beforeunload', function () {
|
||
if (window.changedTests.size > 0) {
|
||
return 'Dialog text here'
|
||
}
|
||
})
|
||
|
||
autosize($('.test-explanation textarea'))
|
||
|
||
function showTestCaseMarker($input, tp, clazz, end) {
|
||
let top = 1e20
|
||
let left = 1e20
|
||
let problem = $input.closest('.problemindexholder')
|
||
$input
|
||
.find('.' + clazz)
|
||
.css('background-color', '#FFFDE7')
|
||
.each(function () {
|
||
top = Math.min(top, $(this).offset().top)
|
||
left = Math.min(left, $(this).offset().left)
|
||
})
|
||
let testCaseMarker = problem.find(
|
||
'.testCaseMarker_' + tp + '_' + end
|
||
)
|
||
if (testCaseMarker.length === 0) {
|
||
const html =
|
||
'<div class="testCaseMarker testCaseMarker_' +
|
||
tp +
|
||
'_' +
|
||
end +
|
||
' notice"></div>'
|
||
problem.append($(html))
|
||
testCaseMarker = problem.find(
|
||
'.testCaseMarker_' + tp + '_' + end
|
||
)
|
||
}
|
||
if (testCaseMarker) {
|
||
testCaseMarker
|
||
.show()
|
||
.offset({ top, left: left - 20 })
|
||
.text(end)
|
||
}
|
||
}
|
||
|
||
$('.test-example-line').hover(
|
||
function () {
|
||
$(this)
|
||
.attr('class')
|
||
.split(' ')
|
||
.forEach((clazz) => {
|
||
if (
|
||
clazz.substr(0, 'test-example-line-'.length) ===
|
||
'test-example-line-'
|
||
) {
|
||
let end = clazz.substr('test-example-line-'.length)
|
||
if (end !== 'even' && end !== 'odd' && end !== '0') {
|
||
showTestCaseMarker(
|
||
$(this).closest('.sample-test').find('.input'),
|
||
'input',
|
||
clazz,
|
||
end
|
||
)
|
||
showTestCaseMarker(
|
||
$(this).closest('.sample-test').find('.output'),
|
||
'output',
|
||
clazz,
|
||
end
|
||
)
|
||
}
|
||
}
|
||
})
|
||
},
|
||
function () {
|
||
$(this)
|
||
.attr('class')
|
||
.split(' ')
|
||
.forEach((clazz) => {
|
||
if (
|
||
clazz.substr(0, 'test-example-line-'.length) ===
|
||
'test-example-line-'
|
||
) {
|
||
let end = clazz.substr('test-example-line-'.length)
|
||
if (end !== 'even' && end !== 'odd' && end !== '0') {
|
||
$('.' + clazz).css('background-color', '')
|
||
$(this)
|
||
.closest('.problemindexholder')
|
||
.find('.testCaseMarker_input_' + end)
|
||
.hide()
|
||
$(this)
|
||
.closest('.problemindexholder')
|
||
.find('.testCaseMarker_output_' + end)
|
||
.hide()
|
||
}
|
||
}
|
||
})
|
||
}
|
||
)
|
||
})
|
||
</script>
|
||
</div>
|
||
<div style="margin-bottom: 2em">
|
||
<div
|
||
class="problemindexholder"
|
||
problemindex="B"
|
||
data-uuid="ps_acba7964483d80b77a40beaf2204266bb81feabd"
|
||
>
|
||
<div
|
||
style="
|
||
display: none;
|
||
margin: 1em 0;
|
||
text-align: center;
|
||
position: relative;
|
||
"
|
||
class="alert alert-info diff-notifier"
|
||
>
|
||
<div>
|
||
The problem statement has recently been changed.
|
||
<a class="view-changes" href="#">View the changes.</a>
|
||
</div>
|
||
<span
|
||
class="diff-notifier-close"
|
||
style="
|
||
position: absolute;
|
||
top: 0.2em;
|
||
right: 0.3em;
|
||
cursor: pointer;
|
||
font-size: 1.4em;
|
||
"
|
||
>×</span
|
||
>
|
||
</div>
|
||
<div class="ttypography">
|
||
<div class="problem-statement">
|
||
<div class="header">
|
||
<div class="title">B. Maximum Cost Deletion</div>
|
||
<div class="time-limit">
|
||
<div class="property-title">time limit per test</div>
|
||
2 seconds
|
||
</div>
|
||
<div class="memory-limit">
|
||
<div class="property-title">memory limit per test</div>
|
||
256 megabytes
|
||
</div>
|
||
<div class="input-file input-standard">
|
||
<div class="property-title">input</div>
|
||
standard input
|
||
</div>
|
||
<div class="output-file output-standard">
|
||
<div class="property-title">output</div>
|
||
standard output
|
||
</div>
|
||
</div>
|
||
<div>
|
||
<p>
|
||
You are given a string
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-281"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-282"
|
||
>s</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-56">
|
||
s
|
||
</script>
|
||
of length
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-283"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-284"
|
||
>n</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-57">
|
||
n
|
||
</script>
|
||
consisting only of the characters
|
||
<span class="tex-font-style-tt">0</span> and
|
||
<span class="tex-font-style-tt">1</span>.
|
||
</p>
|
||
<p>
|
||
You perform the following operation until the string
|
||
becomes empty: choose some
|
||
<span class="tex-font-style-bf">consecutive</span>
|
||
substring of
|
||
<span class="tex-font-style-bf">equal</span> characters,
|
||
erase it from the string and glue the remaining two parts
|
||
together (any of them can be empty) in the same order. For
|
||
example, if you erase the substring
|
||
<span class="tex-font-style-tt">111</span> from the string
|
||
<span class="tex-font-style-tt"
|
||
>1<span class="tex-font-style-bf">111</span>10</span
|
||
>, you will get the string
|
||
<span class="tex-font-style-tt">110</span>. When you
|
||
delete a substring of length
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-285"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-286"
|
||
>l</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-58">
|
||
l
|
||
</script>
|
||
, you get
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-287"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-288"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-289"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>⋅</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-290"
|
||
>l</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-291"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>+</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-292"
|
||
>b</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-59">
|
||
a \cdot l + b
|
||
</script>
|
||
points.
|
||
</p>
|
||
<p>
|
||
Your task is to calculate the maximum number of points
|
||
that you can score in total, if you have to make the given
|
||
string empty.
|
||
</p>
|
||
</div>
|
||
<div class="input-specification">
|
||
<div class="section-title">Input</div>
|
||
<p>
|
||
The first line contains a single integer
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-293"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-294"
|
||
>t</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-60">
|
||
t
|
||
</script>
|
||
(<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-295"
|
||
><span class="MJXp-mn" id="MJXp-Span-296">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-297"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-298"
|
||
>t</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-299"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mn" id="MJXp-Span-300"
|
||
>2000</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-61">
|
||
1 \le t \le 2000
|
||
</script>
|
||
) — the number of testcases.
|
||
</p>
|
||
<p>
|
||
The first line of each testcase contains three integers
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-301"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-302"
|
||
>n</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-62">
|
||
n
|
||
</script>
|
||
,
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-303"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-304"
|
||
>a</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-63">
|
||
a
|
||
</script>
|
||
and
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-305"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-306"
|
||
>b</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-64">
|
||
b
|
||
</script>
|
||
(<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-307"
|
||
><span class="MJXp-mn" id="MJXp-Span-308">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-309"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-310"
|
||
>n</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-311"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mn" id="MJXp-Span-312">100</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-313"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>;</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-314"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>−</span
|
||
><span class="MJXp-mn" id="MJXp-Span-315">100</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-316"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-317"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-318"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-319"
|
||
>b</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-320"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mn" id="MJXp-Span-321"
|
||
>100</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-65">
|
||
1 \le n \le 100; -100 \le a, b \le 100
|
||
</script>
|
||
) — the length of the string
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-322"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-323"
|
||
>s</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-66">
|
||
s
|
||
</script>
|
||
and the parameters
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-324"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-325"
|
||
>a</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-67">
|
||
a
|
||
</script>
|
||
and
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-326"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-327"
|
||
>b</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-68">
|
||
b
|
||
</script>
|
||
.
|
||
</p>
|
||
<p>
|
||
The second line contains the string
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-328"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-329"
|
||
>s</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-69">
|
||
s
|
||
</script>
|
||
. The string
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-330"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-331"
|
||
>s</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-70">
|
||
s
|
||
</script>
|
||
consists only of the characters
|
||
<span class="tex-font-style-tt">0</span> and
|
||
<span class="tex-font-style-tt">1</span>.
|
||
</p>
|
||
</div>
|
||
<div class="output-specification">
|
||
<div class="section-title">Output</div>
|
||
<p>
|
||
For each testcase, print a single integer — the maximum
|
||
number of points that you can score.
|
||
</p>
|
||
</div>
|
||
<div class="sample-tests">
|
||
<div class="section-title">Example</div>
|
||
<div class="sample-test">
|
||
<div class="input">
|
||
<div class="title">
|
||
Input
|
||
<div
|
||
title="Copy"
|
||
data-clipboard-target="#id007675683682124629"
|
||
id="id0006505631406218215"
|
||
class="input-output-copier"
|
||
>
|
||
Copy
|
||
</div>
|
||
</div>
|
||
<pre id="id007675683682124629">
|
||
3
|
||
3 2 0
|
||
000
|
||
5 -2 5
|
||
11001
|
||
6 1 -4
|
||
100111
|
||
</pre
|
||
>
|
||
</div>
|
||
<div class="output">
|
||
<div class="title">
|
||
Output
|
||
<div
|
||
title="Copy"
|
||
data-clipboard-target="#id001322358127831661"
|
||
id="id00996265197942917"
|
||
class="input-output-copier"
|
||
>
|
||
Copy
|
||
</div>
|
||
</div>
|
||
<pre id="id001322358127831661">
|
||
6
|
||
15
|
||
-2
|
||
</pre
|
||
>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<div class="note">
|
||
<div class="section-title">Note</div>
|
||
<p>
|
||
In the first example, it is enough to delete the entire
|
||
string, then we will get
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-332"
|
||
><span class="MJXp-mn" id="MJXp-Span-333">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-334"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>⋅</span
|
||
><span class="MJXp-mn" id="MJXp-Span-335">3</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-336"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>+</span
|
||
><span class="MJXp-mn" id="MJXp-Span-337">0</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-338"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>=</span
|
||
><span class="MJXp-mn" id="MJXp-Span-339"
|
||
>6</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-71">
|
||
2 \cdot 3 + 0 = 6
|
||
</script>
|
||
points.
|
||
</p>
|
||
<p>
|
||
In the second example, if we delete characters one by one,
|
||
then for each deleted character we will get
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-340"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-341"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-342"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>−</span
|
||
><span class="MJXp-mn" id="MJXp-Span-343">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-344"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-345"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>⋅</span
|
||
><span class="MJXp-mn" id="MJXp-Span-346">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-347"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>+</span
|
||
><span class="MJXp-mn" id="MJXp-Span-348">5</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-349"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>=</span
|
||
><span class="MJXp-mn" id="MJXp-Span-350"
|
||
>3</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-72">
|
||
(-2) \cdot 1 + 5 = 3
|
||
</script>
|
||
points, i. e.
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-351"
|
||
><span class="MJXp-mn" id="MJXp-Span-352"
|
||
>15</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-73">
|
||
15
|
||
</script>
|
||
points in total.
|
||
</p>
|
||
<p>
|
||
In the third example, we can delete the substring
|
||
<span class="tex-font-style-tt">00</span> from the string
|
||
<span class="tex-font-style-tt"
|
||
>1<span class="tex-font-style-bf">00</span>111</span
|
||
>, we get
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-353"
|
||
><span class="MJXp-mn" id="MJXp-Span-354">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-355"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>⋅</span
|
||
><span class="MJXp-mn" id="MJXp-Span-356">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-357"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>+</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-358"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-359"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>−</span
|
||
><span class="MJXp-mn" id="MJXp-Span-360">4</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-361"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-362"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>=</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-363"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>−</span
|
||
><span class="MJXp-mn" id="MJXp-Span-364"
|
||
>2</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-74">
|
||
1 \cdot 2 + (-4) = -2
|
||
</script>
|
||
points, and the string will be equal to
|
||
<span class="tex-font-style-tt">1111</span>, removing it
|
||
entirely we get
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-365"
|
||
><span class="MJXp-mn" id="MJXp-Span-366">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-367"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>⋅</span
|
||
><span class="MJXp-mn" id="MJXp-Span-368">4</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-369"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>+</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-370"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-371"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>−</span
|
||
><span class="MJXp-mn" id="MJXp-Span-372">4</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-373"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-374"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>=</span
|
||
><span class="MJXp-mn" id="MJXp-Span-375"
|
||
>0</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-75">
|
||
1 \cdot 4 + (-4) = 0
|
||
</script>
|
||
points. In total, we got
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-376"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-377"
|
||
style="margin-left: 0em; margin-right: 0.111em"
|
||
>−</span
|
||
><span class="MJXp-mn" id="MJXp-Span-378"
|
||
>2</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-76">
|
||
-2
|
||
</script>
|
||
points for
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-379"
|
||
><span class="MJXp-mn" id="MJXp-Span-380"
|
||
>2</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-77">
|
||
2
|
||
</script>
|
||
operations.
|
||
</p>
|
||
</div>
|
||
</div>
|
||
<p></p>
|
||
</div>
|
||
</div>
|
||
|
||
<script>
|
||
$(function () {
|
||
Codeforces.addMathJaxListener(function () {
|
||
let $problem = $('div[problemindex=B]')
|
||
let uuid = $problem.attr('data-uuid')
|
||
let statementText = convertStatementToText(
|
||
$problem.find('.ttypography').get(0)
|
||
)
|
||
|
||
let previousStatementText = Codeforces.getFromStorage(uuid)
|
||
if (previousStatementText) {
|
||
if (previousStatementText !== statementText) {
|
||
$problem.find('.diff-notifier').show()
|
||
|
||
$problem.find('.diff-notifier-close').click(function () {
|
||
Codeforces.putToStorageTtl(
|
||
uuid,
|
||
statementText,
|
||
6 * 60 * 60
|
||
)
|
||
$problem.find('.diff-notifier').hide()
|
||
})
|
||
|
||
$problem.find('a.view-changes').click(function () {
|
||
$.post(
|
||
'/data/diff',
|
||
{
|
||
action: 'getDiff',
|
||
a: previousStatementText,
|
||
b: statementText
|
||
},
|
||
function (result) {
|
||
if (result['success'] === 'true') {
|
||
Codeforces.facebox(
|
||
'.diff-popup',
|
||
'//codeforces.org/s/15523'
|
||
)
|
||
$('#facebox .diff-popup').html(result['diff'])
|
||
}
|
||
},
|
||
'json'
|
||
)
|
||
})
|
||
}
|
||
} else {
|
||
Codeforces.putToStorageTtl(uuid, statementText, 6 * 60 * 60)
|
||
}
|
||
})
|
||
})
|
||
</script>
|
||
<script type="text/javascript">
|
||
$(document).ready(function () {
|
||
const inputFileDiv = $('div.input-file')
|
||
const inputFile = inputFileDiv.text()
|
||
const outputFileDiv = $('div.output-file')
|
||
const outputFile = outputFileDiv.text()
|
||
|
||
if (
|
||
!endsWith(inputFile, 'standard input') &&
|
||
!endsWith(inputFile, 'standard input')
|
||
) {
|
||
inputFileDiv.attr('style', 'font-weight: bold')
|
||
}
|
||
|
||
if (
|
||
!endsWith(outputFile, 'standard output') &&
|
||
!endsWith(outputFile, 'standard output')
|
||
) {
|
||
outputFileDiv.attr('style', 'font-weight: bold')
|
||
}
|
||
|
||
const titleDiv = $('div.header div.title')
|
||
})
|
||
</script>
|
||
</div>
|
||
<div style="margin-bottom: 2em">
|
||
<div
|
||
class="problemindexholder"
|
||
problemindex="C"
|
||
data-uuid="ps_b3e37fec06e987daeb69fa1795897de33dc060d7"
|
||
>
|
||
<div
|
||
style="
|
||
display: none;
|
||
margin: 1em 0;
|
||
text-align: center;
|
||
position: relative;
|
||
"
|
||
class="alert alert-info diff-notifier"
|
||
>
|
||
<div>
|
||
The problem statement has recently been changed.
|
||
<a class="view-changes" href="#">View the changes.</a>
|
||
</div>
|
||
<span
|
||
class="diff-notifier-close"
|
||
style="
|
||
position: absolute;
|
||
top: 0.2em;
|
||
right: 0.3em;
|
||
cursor: pointer;
|
||
font-size: 1.4em;
|
||
"
|
||
>×</span
|
||
>
|
||
</div>
|
||
<div class="ttypography">
|
||
<div class="problem-statement">
|
||
<div class="header">
|
||
<div class="title">C. Manhattan Subarrays</div>
|
||
<div class="time-limit">
|
||
<div class="property-title">time limit per test</div>
|
||
2 seconds
|
||
</div>
|
||
<div class="memory-limit">
|
||
<div class="property-title">memory limit per test</div>
|
||
256 megabytes
|
||
</div>
|
||
<div class="input-file input-standard">
|
||
<div class="property-title">input</div>
|
||
standard input
|
||
</div>
|
||
<div class="output-file output-standard">
|
||
<div class="property-title">output</div>
|
||
standard output
|
||
</div>
|
||
</div>
|
||
<div>
|
||
<p>
|
||
Suppose you have two points
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-381"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-382"
|
||
>p</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-383"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>=</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-384"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-385"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-386"
|
||
style="margin-right: 0.05em"
|
||
>x</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-387"
|
||
style="vertical-align: -0.4em"
|
||
>p</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-388"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-389"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-390"
|
||
style="margin-right: 0.05em"
|
||
>y</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-391"
|
||
style="vertical-align: -0.4em"
|
||
>p</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-392"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-78">
|
||
p = (x_p, y_p)
|
||
</script>
|
||
and
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-393"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-394"
|
||
>q</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-395"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>=</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-396"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-397"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-398"
|
||
style="margin-right: 0.05em"
|
||
>x</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-399"
|
||
style="vertical-align: -0.4em"
|
||
>q</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-400"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-401"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-402"
|
||
style="margin-right: 0.05em"
|
||
>y</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-403"
|
||
style="vertical-align: -0.4em"
|
||
>q</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-404"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-79">
|
||
q = (x_q, y_q)
|
||
</script>
|
||
. Let's denote the Manhattan distance between them as
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-405"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-406"
|
||
>d</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-407"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-408"
|
||
>p</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-409"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-410"
|
||
>q</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-411"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-412"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>=</span
|
||
><span class="MJXp-mrow" id="MJXp-Span-413"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-414"
|
||
style="
|
||
margin-left: 0.167em;
|
||
margin-right: 0.167em;
|
||
"
|
||
>|</span
|
||
></span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-415"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-416"
|
||
style="margin-right: 0.05em"
|
||
>x</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-417"
|
||
style="vertical-align: -0.4em"
|
||
>p</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-418"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>−</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-419"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-420"
|
||
style="margin-right: 0.05em"
|
||
>x</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-421"
|
||
style="vertical-align: -0.4em"
|
||
>q</span
|
||
></span
|
||
><span class="MJXp-mrow" id="MJXp-Span-422"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-423"
|
||
style="
|
||
margin-left: 0.167em;
|
||
margin-right: 0.167em;
|
||
"
|
||
>|</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-424"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>+</span
|
||
><span class="MJXp-mrow" id="MJXp-Span-425"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-426"
|
||
style="
|
||
margin-left: 0.167em;
|
||
margin-right: 0.167em;
|
||
"
|
||
>|</span
|
||
></span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-427"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-428"
|
||
style="margin-right: 0.05em"
|
||
>y</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-429"
|
||
style="vertical-align: -0.4em"
|
||
>p</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-430"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>−</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-431"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-432"
|
||
style="margin-right: 0.05em"
|
||
>y</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-433"
|
||
style="vertical-align: -0.4em"
|
||
>q</span
|
||
></span
|
||
><span class="MJXp-mrow" id="MJXp-Span-434"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-435"
|
||
style="
|
||
margin-left: 0.167em;
|
||
margin-right: 0.167em;
|
||
"
|
||
>|</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-80">
|
||
d(p, q) = |x_p - x_q| + |y_p - y_q|
|
||
</script>
|
||
.
|
||
</p>
|
||
<p>
|
||
Let's say that three points
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-436"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-437"
|
||
>p</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-81">
|
||
p
|
||
</script>
|
||
,
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-438"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-439"
|
||
>q</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-82">
|
||
q
|
||
</script>
|
||
,
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-440"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-441"
|
||
>r</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-83">
|
||
r
|
||
</script>
|
||
form a <span class="tex-font-style-it">bad</span> triple
|
||
if
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-442"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-443"
|
||
>d</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-444"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-445"
|
||
>p</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-446"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-447"
|
||
>r</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-448"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-449"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>=</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-450"
|
||
>d</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-451"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-452"
|
||
>p</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-453"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-454"
|
||
>q</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-455"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-456"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>+</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-457"
|
||
>d</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-458"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-459"
|
||
>q</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-460"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-461"
|
||
>r</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-462"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-84">
|
||
d(p, r) = d(p, q) + d(q, r)
|
||
</script>
|
||
.
|
||
</p>
|
||
<p>
|
||
Let's say that an array
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-463"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-464"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-465"
|
||
style="margin-right: 0.05em"
|
||
>b</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-466"
|
||
style="vertical-align: -0.4em"
|
||
>1</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-467"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-468"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-469"
|
||
style="margin-right: 0.05em"
|
||
>b</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-470"
|
||
style="vertical-align: -0.4em"
|
||
>2</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-471"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-472"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>…</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-473"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-474"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-475"
|
||
style="margin-right: 0.05em"
|
||
>b</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-476"
|
||
style="vertical-align: -0.4em"
|
||
>m</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-85">
|
||
b_1, b_2, \dots, b_m
|
||
</script>
|
||
is <span class="tex-font-style-it">good</span> if it is
|
||
impossible to choose three
|
||
<span class="tex-font-style-bf">distinct</span> indices
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-477"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-478"
|
||
>i</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-86">
|
||
i
|
||
</script>
|
||
,
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-479"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-480"
|
||
>j</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-87">
|
||
j
|
||
</script>
|
||
,
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-481"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-482"
|
||
>k</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-88">
|
||
k
|
||
</script>
|
||
such that the points
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-483"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-484"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-485"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-486"
|
||
style="margin-right: 0.05em"
|
||
>b</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-487"
|
||
style="vertical-align: -0.4em"
|
||
>i</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-488"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-489"
|
||
>i</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-490"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-89">
|
||
(b_i, i)
|
||
</script>
|
||
,
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-491"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-492"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-493"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-494"
|
||
style="margin-right: 0.05em"
|
||
>b</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-495"
|
||
style="vertical-align: -0.4em"
|
||
>j</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-496"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-497"
|
||
>j</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-498"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-90">
|
||
(b_j, j)
|
||
</script>
|
||
and
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-499"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-500"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-501"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-502"
|
||
style="margin-right: 0.05em"
|
||
>b</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-503"
|
||
style="vertical-align: -0.4em"
|
||
>k</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-504"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-505"
|
||
>k</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-506"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-91">
|
||
(b_k, k)
|
||
</script>
|
||
form a bad triple.
|
||
</p>
|
||
<p>
|
||
You are given an array
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-507"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-508"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-509"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-510"
|
||
style="vertical-align: -0.4em"
|
||
>1</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-511"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-512"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-513"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-514"
|
||
style="vertical-align: -0.4em"
|
||
>2</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-515"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-516"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>…</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-517"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-518"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-519"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-520"
|
||
style="vertical-align: -0.4em"
|
||
>n</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-92">
|
||
a_1, a_2, \dots, a_n
|
||
</script>
|
||
. Calculate the number of
|
||
<span class="tex-font-style-it">good</span> subarrays of
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-521"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-522"
|
||
>a</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-93">
|
||
a
|
||
</script>
|
||
. A subarray of the array
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-523"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-524"
|
||
>a</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-94">
|
||
a
|
||
</script>
|
||
is the array
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-525"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-526"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-527"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-528"
|
||
style="vertical-align: -0.4em"
|
||
>l</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-529"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-530"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-531"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mrow MJXp-script"
|
||
id="MJXp-Span-532"
|
||
style="vertical-align: -0.4em"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-533"
|
||
>l</span
|
||
><span class="MJXp-mo" id="MJXp-Span-534">+</span
|
||
><span class="MJXp-mn" id="MJXp-Span-535"
|
||
>1</span
|
||
></span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-536"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-537"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>…</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-538"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-539"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-540"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-541"
|
||
style="vertical-align: -0.4em"
|
||
>r</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-95">
|
||
a_l, a_{l + 1}, \dots, a_r
|
||
</script>
|
||
for some
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-542"
|
||
><span class="MJXp-mn" id="MJXp-Span-543">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-544"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-545"
|
||
>l</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-546"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-547"
|
||
>r</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-548"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-549"
|
||
>n</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-96">
|
||
1 \le l \le r \le n
|
||
</script>
|
||
.
|
||
</p>
|
||
<p>
|
||
Note that, according to the definition, subarrays of
|
||
length
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-550"
|
||
><span class="MJXp-mn" id="MJXp-Span-551"
|
||
>1</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-97">
|
||
1
|
||
</script>
|
||
and
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-552"
|
||
><span class="MJXp-mn" id="MJXp-Span-553"
|
||
>2</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-98">
|
||
2
|
||
</script>
|
||
are <span class="tex-font-style-it">good</span>.
|
||
</p>
|
||
</div>
|
||
<div class="input-specification">
|
||
<div class="section-title">Input</div>
|
||
<p>
|
||
The first line contains one integer
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-554"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-555"
|
||
>t</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-99">
|
||
t
|
||
</script>
|
||
(<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-556"
|
||
><span class="MJXp-mn" id="MJXp-Span-557">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-558"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-559"
|
||
>t</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-560"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mn" id="MJXp-Span-561"
|
||
>5000</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-100">
|
||
1 \le t \le 5000
|
||
</script>
|
||
) — the number of test cases.
|
||
</p>
|
||
<p>
|
||
The first line of each test case contains one integer
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-562"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-563"
|
||
>n</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-101">
|
||
n
|
||
</script>
|
||
(<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-564"
|
||
><span class="MJXp-mn" id="MJXp-Span-565">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-566"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-567"
|
||
>n</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-568"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mn" id="MJXp-Span-569">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-570"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>⋅</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-571"
|
||
><span
|
||
class="MJXp-mn"
|
||
id="MJXp-Span-572"
|
||
style="margin-right: 0.05em"
|
||
>10</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-573"
|
||
style="vertical-align: 0.5em"
|
||
>5</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-102">
|
||
1 \le n \le 2 \cdot 10^5
|
||
</script>
|
||
) — the length of array
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-574"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-575"
|
||
>a</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-103">
|
||
a
|
||
</script>
|
||
.
|
||
</p>
|
||
<p>
|
||
The second line of each test case contains
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-576"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-577"
|
||
>n</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-104">
|
||
n
|
||
</script>
|
||
integers
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-578"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-579"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-580"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-581"
|
||
style="vertical-align: -0.4em"
|
||
>1</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-582"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-583"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-584"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-585"
|
||
style="vertical-align: -0.4em"
|
||
>2</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-586"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-587"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>…</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-588"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-589"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-590"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-591"
|
||
style="vertical-align: -0.4em"
|
||
>n</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-105">
|
||
a_1, a_2, \dots, a_n
|
||
</script>
|
||
(<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-592"
|
||
><span class="MJXp-mn" id="MJXp-Span-593">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-594"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-595"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-596"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-597"
|
||
style="vertical-align: -0.4em"
|
||
>i</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-598"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-599"
|
||
><span
|
||
class="MJXp-mn"
|
||
id="MJXp-Span-600"
|
||
style="margin-right: 0.05em"
|
||
>10</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-601"
|
||
style="vertical-align: 0.5em"
|
||
>9</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-106">
|
||
1 \le a_i \le 10^9
|
||
</script>
|
||
).
|
||
</p>
|
||
<p>
|
||
It's guaranteed that the sum of
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-602"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-603"
|
||
>n</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-107">
|
||
n
|
||
</script>
|
||
doesn't exceed
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-604"
|
||
><span class="MJXp-mn" id="MJXp-Span-605">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-606"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>⋅</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-607"
|
||
><span
|
||
class="MJXp-mn"
|
||
id="MJXp-Span-608"
|
||
style="margin-right: 0.05em"
|
||
>10</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-609"
|
||
style="vertical-align: 0.5em"
|
||
>5</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-108">
|
||
2 \cdot 10^5
|
||
</script>
|
||
.
|
||
</p>
|
||
</div>
|
||
<div class="output-specification">
|
||
<div class="section-title">Output</div>
|
||
<p>
|
||
For each test case, print the number of
|
||
<span class="tex-font-style-it">good</span> subarrays of
|
||
array
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-610"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-611"
|
||
>a</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-109">
|
||
a
|
||
</script>
|
||
.
|
||
</p>
|
||
</div>
|
||
<div class="sample-tests">
|
||
<div class="section-title">Example</div>
|
||
<div class="sample-test">
|
||
<div class="input">
|
||
<div class="title">
|
||
Input
|
||
<div
|
||
title="Copy"
|
||
data-clipboard-target="#id0045100789178148193"
|
||
id="id0034855463835277845"
|
||
class="input-output-copier"
|
||
>
|
||
Copy
|
||
</div>
|
||
</div>
|
||
<pre id="id0045100789178148193">
|
||
3
|
||
4
|
||
2 4 1 3
|
||
5
|
||
6 9 1 9 6
|
||
2
|
||
13 37
|
||
</pre
|
||
>
|
||
</div>
|
||
<div class="output">
|
||
<div class="title">
|
||
Output
|
||
<div
|
||
title="Copy"
|
||
data-clipboard-target="#id008205050640892653"
|
||
id="id00646096671878121"
|
||
class="input-output-copier"
|
||
>
|
||
Copy
|
||
</div>
|
||
</div>
|
||
<pre id="id008205050640892653">
|
||
10
|
||
12
|
||
3
|
||
</pre
|
||
>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<div class="note">
|
||
<div class="section-title">Note</div>
|
||
<p>
|
||
In the first test case, it can be proven that any subarray
|
||
of
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-612"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-613"
|
||
>a</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-110">
|
||
a
|
||
</script>
|
||
is <span class="tex-font-style-it">good</span>. For
|
||
example, subarray
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-614"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-615"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>[</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-616"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-617"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-618"
|
||
style="vertical-align: -0.4em"
|
||
>2</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-619"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-620"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-621"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-622"
|
||
style="vertical-align: -0.4em"
|
||
>3</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-623"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-624"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-625"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-626"
|
||
style="vertical-align: -0.4em"
|
||
>4</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-627"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>]</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-111">
|
||
[a_2, a_3, a_4]
|
||
</script>
|
||
is good since it contains only three elements and:
|
||
</p>
|
||
<ul>
|
||
<li>
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-628"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-629"
|
||
>d</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-630"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-631"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-632"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-633"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-634"
|
||
style="vertical-align: -0.4em"
|
||
>2</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-635"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-636">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-637"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-638"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-639"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-640"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-641"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-642"
|
||
style="vertical-align: -0.4em"
|
||
>4</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-643"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-644">4</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-645"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-646"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-647"
|
||
style="
|
||
margin-left: 0.333em;
|
||
margin-right: 0.333em;
|
||
"
|
||
>=</span
|
||
><span class="MJXp-mrow" id="MJXp-Span-648"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-649"
|
||
style="
|
||
margin-left: 0.167em;
|
||
margin-right: 0.167em;
|
||
"
|
||
>|</span
|
||
></span
|
||
><span class="MJXp-mn" id="MJXp-Span-650">4</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-651"
|
||
style="
|
||
margin-left: 0.267em;
|
||
margin-right: 0.267em;
|
||
"
|
||
>−</span
|
||
><span class="MJXp-mn" id="MJXp-Span-652">3</span
|
||
><span class="MJXp-mrow" id="MJXp-Span-653"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-654"
|
||
style="
|
||
margin-left: 0.167em;
|
||
margin-right: 0.167em;
|
||
"
|
||
>|</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-655"
|
||
style="
|
||
margin-left: 0.267em;
|
||
margin-right: 0.267em;
|
||
"
|
||
>+</span
|
||
><span class="MJXp-mrow" id="MJXp-Span-656"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-657"
|
||
style="
|
||
margin-left: 0.167em;
|
||
margin-right: 0.167em;
|
||
"
|
||
>|</span
|
||
></span
|
||
><span class="MJXp-mn" id="MJXp-Span-658">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-659"
|
||
style="
|
||
margin-left: 0.267em;
|
||
margin-right: 0.267em;
|
||
"
|
||
>−</span
|
||
><span class="MJXp-mn" id="MJXp-Span-660">4</span
|
||
><span class="MJXp-mrow" id="MJXp-Span-661"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-662"
|
||
style="
|
||
margin-left: 0.167em;
|
||
margin-right: 0.167em;
|
||
"
|
||
>|</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-663"
|
||
style="
|
||
margin-left: 0.333em;
|
||
margin-right: 0.333em;
|
||
"
|
||
>=</span
|
||
><span class="MJXp-mn" id="MJXp-Span-664"
|
||
>3</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-112">
|
||
d((a_2, 2), (a_4, 4)) = |4 - 3| + |2 - 4| = 3
|
||
</script>
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-665"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-666"
|
||
style="
|
||
margin-left: 0.333em;
|
||
margin-right: 0.333em;
|
||
"
|
||
><</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-113">
|
||
<
|
||
</script>
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-667"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-668"
|
||
>d</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-669"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-670"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-671"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-672"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-673"
|
||
style="vertical-align: -0.4em"
|
||
>2</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-674"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-675">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-676"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-677"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-678"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-679"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-680"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-681"
|
||
style="vertical-align: -0.4em"
|
||
>3</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-682"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-683">3</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-684"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-685"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-686"
|
||
style="
|
||
margin-left: 0.267em;
|
||
margin-right: 0.267em;
|
||
"
|
||
>+</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-687"
|
||
>d</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-688"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-689"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-690"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-691"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-692"
|
||
style="vertical-align: -0.4em"
|
||
>3</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-693"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
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|
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|
||
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|
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|
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|
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|
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|
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||
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|
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|
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|
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|
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|
||
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|
||
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|
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|
||
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|
||
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|
||
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|
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||
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|
||
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|
||
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|
||
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|
||
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|
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
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|
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|
||
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|
||
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||
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|
||
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|
||
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|
||
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|
||
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|
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|
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
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|
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|
||
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|
||
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|
||
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|
||
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|
||
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|
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|
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|
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|
||
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|
||
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|
||
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|
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
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|
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|
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|
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|
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|
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|
||
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|
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|
||
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|
||
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|
||
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|
||
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||
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|
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|
||
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|
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|
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|
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|
||
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|
||
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|
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|
||
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|
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|
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||
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||
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|
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|
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|
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||
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|
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|
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|
||
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|
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
||
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|
||
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|
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|
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|
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|
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|
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|
||
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|
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|
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|
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|
||
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|
||
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|
||
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||
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|
||
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|
||
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|
||
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|
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|
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|
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|
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|
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|
||
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|
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|
||
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|
||
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|
||
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|
||
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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||
><span class="MJXp-msubsup" id="MJXp-Span-799"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-800"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-801"
|
||
style="vertical-align: -0.4em"
|
||
>3</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-802"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-803">3</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-804"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-805"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-806"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-807"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-808"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-809"
|
||
style="vertical-align: -0.4em"
|
||
>2</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-810"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-811">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-812"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-813"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-814"
|
||
style="
|
||
margin-left: 0.267em;
|
||
margin-right: 0.267em;
|
||
"
|
||
>+</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-815"
|
||
>d</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-816"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-817"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-818"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-819"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-820"
|
||
style="vertical-align: -0.4em"
|
||
>2</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-821"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-822">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-823"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-824"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-825"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-826"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-827"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-828"
|
||
style="vertical-align: -0.4em"
|
||
>4</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-829"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-830">4</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-831"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-832"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-120">
|
||
d((a_3, 3), (a_2, 2)) + d((a_2, 2), (a_4, 4))
|
||
</script>
|
||
;
|
||
</li>
|
||
</ul>
|
||
<p>
|
||
In the second test case, for example, subarray
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-833"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-834"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>[</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-835"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-836"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-837"
|
||
style="vertical-align: -0.4em"
|
||
>1</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-838"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-839"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-840"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-841"
|
||
style="vertical-align: -0.4em"
|
||
>2</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-842"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-843"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-844"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-845"
|
||
style="vertical-align: -0.4em"
|
||
>3</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-846"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-847"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-848"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-849"
|
||
style="vertical-align: -0.4em"
|
||
>4</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-850"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>]</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-121">
|
||
[a_1, a_2, a_3, a_4]
|
||
</script>
|
||
is <span class="tex-font-style-bf">not</span> good, since
|
||
it contains a
|
||
<span class="tex-font-style-it">bad</span> triple
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-851"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-852"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-853"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-854"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-855"
|
||
style="vertical-align: -0.4em"
|
||
>1</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-856"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-857">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-858"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-122">
|
||
(a_1, 1)
|
||
</script>
|
||
,
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-859"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-860"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-861"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-862"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-863"
|
||
style="vertical-align: -0.4em"
|
||
>2</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-864"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-865">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-866"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-123">
|
||
(a_2, 2)
|
||
</script>
|
||
,
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-867"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-868"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-869"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-870"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-871"
|
||
style="vertical-align: -0.4em"
|
||
>4</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-872"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-873">4</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-874"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-124">
|
||
(a_4, 4)
|
||
</script>
|
||
:
|
||
</p>
|
||
<ul>
|
||
<li>
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-875"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-876"
|
||
>d</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-877"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-878"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-879"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-880"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-881"
|
||
style="vertical-align: -0.4em"
|
||
>1</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-882"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-883">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-884"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-885"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-886"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-887"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-888"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-889"
|
||
style="vertical-align: -0.4em"
|
||
>4</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-890"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-891">4</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-892"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-893"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-894"
|
||
style="
|
||
margin-left: 0.333em;
|
||
margin-right: 0.333em;
|
||
"
|
||
>=</span
|
||
><span class="MJXp-mrow" id="MJXp-Span-895"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-896"
|
||
style="
|
||
margin-left: 0.167em;
|
||
margin-right: 0.167em;
|
||
"
|
||
>|</span
|
||
></span
|
||
><span class="MJXp-mn" id="MJXp-Span-897">6</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-898"
|
||
style="
|
||
margin-left: 0.267em;
|
||
margin-right: 0.267em;
|
||
"
|
||
>−</span
|
||
><span class="MJXp-mn" id="MJXp-Span-899">9</span
|
||
><span class="MJXp-mrow" id="MJXp-Span-900"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-901"
|
||
style="
|
||
margin-left: 0.167em;
|
||
margin-right: 0.167em;
|
||
"
|
||
>|</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-902"
|
||
style="
|
||
margin-left: 0.267em;
|
||
margin-right: 0.267em;
|
||
"
|
||
>+</span
|
||
><span class="MJXp-mrow" id="MJXp-Span-903"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-904"
|
||
style="
|
||
margin-left: 0.167em;
|
||
margin-right: 0.167em;
|
||
"
|
||
>|</span
|
||
></span
|
||
><span class="MJXp-mn" id="MJXp-Span-905">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-906"
|
||
style="
|
||
margin-left: 0.267em;
|
||
margin-right: 0.267em;
|
||
"
|
||
>−</span
|
||
><span class="MJXp-mn" id="MJXp-Span-907">4</span
|
||
><span class="MJXp-mrow" id="MJXp-Span-908"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-909"
|
||
style="
|
||
margin-left: 0.167em;
|
||
margin-right: 0.167em;
|
||
"
|
||
>|</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-910"
|
||
style="
|
||
margin-left: 0.333em;
|
||
margin-right: 0.333em;
|
||
"
|
||
>=</span
|
||
><span class="MJXp-mn" id="MJXp-Span-911"
|
||
>6</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-125">
|
||
d((a_1, 1), (a_4, 4)) = |6 - 9| + |1 - 4| = 6
|
||
</script>
|
||
;
|
||
</li>
|
||
<li>
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-912"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-913"
|
||
>d</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-914"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
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|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-915"
|
||
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|
||
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|
||
><span class="MJXp-msubsup" id="MJXp-Span-916"
|
||
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|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-917"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-918"
|
||
style="vertical-align: -0.4em"
|
||
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|
||
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|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-919"
|
||
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|
||
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|
||
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|
||
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|
||
class="MJXp-mo"
|
||
id="MJXp-Span-921"
|
||
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|
||
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|
||
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|
||
class="MJXp-mo"
|
||
id="MJXp-Span-922"
|
||
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|
||
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|
||
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|
||
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|
||
id="MJXp-Span-923"
|
||
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|
||
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|
||
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|
||
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|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-925"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-926"
|
||
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|
||
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|
||
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|
||
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|
||
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|
||
id="MJXp-Span-927"
|
||
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|
||
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|
||
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|
||
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|
||
class="MJXp-mo"
|
||
id="MJXp-Span-929"
|
||
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|
||
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|
||
><span
|
||
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|
||
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|
||
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|
||
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|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-931"
|
||
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|
||
margin-left: 0.333em;
|
||
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|
||
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|
||
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|
||
><span class="MJXp-mrow" id="MJXp-Span-932"
|
||
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|
||
class="MJXp-mo"
|
||
id="MJXp-Span-933"
|
||
style="
|
||
margin-left: 0.167em;
|
||
margin-right: 0.167em;
|
||
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|
||
>|</span
|
||
></span
|
||
><span class="MJXp-mn" id="MJXp-Span-934">6</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-935"
|
||
style="
|
||
margin-left: 0.267em;
|
||
margin-right: 0.267em;
|
||
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|
||
>−</span
|
||
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|
||
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|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-938"
|
||
style="
|
||
margin-left: 0.167em;
|
||
margin-right: 0.167em;
|
||
"
|
||
>|</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-939"
|
||
style="
|
||
margin-left: 0.267em;
|
||
margin-right: 0.267em;
|
||
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|
||
>+</span
|
||
><span class="MJXp-mrow" id="MJXp-Span-940"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-941"
|
||
style="
|
||
margin-left: 0.167em;
|
||
margin-right: 0.167em;
|
||
"
|
||
>|</span
|
||
></span
|
||
><span class="MJXp-mn" id="MJXp-Span-942">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-943"
|
||
style="
|
||
margin-left: 0.267em;
|
||
margin-right: 0.267em;
|
||
"
|
||
>−</span
|
||
><span class="MJXp-mn" id="MJXp-Span-944">2</span
|
||
><span class="MJXp-mrow" id="MJXp-Span-945"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-946"
|
||
style="
|
||
margin-left: 0.167em;
|
||
margin-right: 0.167em;
|
||
"
|
||
>|</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-947"
|
||
style="
|
||
margin-left: 0.333em;
|
||
margin-right: 0.333em;
|
||
"
|
||
>=</span
|
||
><span class="MJXp-mn" id="MJXp-Span-948"
|
||
>4</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-126">
|
||
d((a_1, 1), (a_2, 2)) = |6 - 9| + |1 - 2| = 4
|
||
</script>
|
||
;
|
||
</li>
|
||
<li>
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-949"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-950"
|
||
>d</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-951"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
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|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-952"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-953"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-954"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-955"
|
||
style="vertical-align: -0.4em"
|
||
>2</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-956"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
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|
||
><span class="MJXp-mn" id="MJXp-Span-957">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-958"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-959"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
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|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-960"
|
||
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|
||
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|
||
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|
||
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|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-962"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-963"
|
||
style="vertical-align: -0.4em"
|
||
>4</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-964"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
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|
||
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|
||
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|
||
class="MJXp-mo"
|
||
id="MJXp-Span-966"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
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|
||
class="MJXp-mo"
|
||
id="MJXp-Span-967"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
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|
||
class="MJXp-mo"
|
||
id="MJXp-Span-968"
|
||
style="
|
||
margin-left: 0.333em;
|
||
margin-right: 0.333em;
|
||
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|
||
>=</span
|
||
><span class="MJXp-mrow" id="MJXp-Span-969"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-970"
|
||
style="
|
||
margin-left: 0.167em;
|
||
margin-right: 0.167em;
|
||
"
|
||
>|</span
|
||
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|
||
><span class="MJXp-mn" id="MJXp-Span-971">9</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-972"
|
||
style="
|
||
margin-left: 0.267em;
|
||
margin-right: 0.267em;
|
||
"
|
||
>−</span
|
||
><span class="MJXp-mn" id="MJXp-Span-973">9</span
|
||
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|
||
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|
||
class="MJXp-mo"
|
||
id="MJXp-Span-975"
|
||
style="
|
||
margin-left: 0.167em;
|
||
margin-right: 0.167em;
|
||
"
|
||
>|</span
|
||
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|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-976"
|
||
style="
|
||
margin-left: 0.267em;
|
||
margin-right: 0.267em;
|
||
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|
||
>+</span
|
||
><span class="MJXp-mrow" id="MJXp-Span-977"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-978"
|
||
style="
|
||
margin-left: 0.167em;
|
||
margin-right: 0.167em;
|
||
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|
||
>|</span
|
||
></span
|
||
><span class="MJXp-mn" id="MJXp-Span-979">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-980"
|
||
style="
|
||
margin-left: 0.267em;
|
||
margin-right: 0.267em;
|
||
"
|
||
>−</span
|
||
><span class="MJXp-mn" id="MJXp-Span-981">4</span
|
||
><span class="MJXp-mrow" id="MJXp-Span-982"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-983"
|
||
style="
|
||
margin-left: 0.167em;
|
||
margin-right: 0.167em;
|
||
"
|
||
>|</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-984"
|
||
style="
|
||
margin-left: 0.333em;
|
||
margin-right: 0.333em;
|
||
"
|
||
>=</span
|
||
><span class="MJXp-mn" id="MJXp-Span-985"
|
||
>2</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-127">
|
||
d((a_2, 2), (a_4, 4)) = |9 - 9| + |2 - 4| = 2
|
||
</script>
|
||
;
|
||
</li>
|
||
</ul>
|
||
<p>
|
||
So,
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-986"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-987"
|
||
>d</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-988"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
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|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-989"
|
||
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|
||
>(</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-990"
|
||
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|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-991"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-992"
|
||
style="vertical-align: -0.4em"
|
||
>1</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-993"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
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|
||
><span class="MJXp-mn" id="MJXp-Span-994">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-995"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-996"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-997"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-998"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-999"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-1000"
|
||
style="vertical-align: -0.4em"
|
||
>4</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1001"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1002">4</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1003"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1004"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1005"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>=</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1006"
|
||
>d</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1007"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1008"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1009"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1010"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-1011"
|
||
style="vertical-align: -0.4em"
|
||
>1</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1012"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1013">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1014"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1015"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1016"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1017"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1018"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-1019"
|
||
style="vertical-align: -0.4em"
|
||
>2</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1020"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1021">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1022"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1023"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1024"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>+</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1025"
|
||
>d</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1026"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1027"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1028"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1029"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-1030"
|
||
style="vertical-align: -0.4em"
|
||
>2</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1031"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1032">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1033"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1034"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1035"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1036"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1037"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-1038"
|
||
style="vertical-align: -0.4em"
|
||
>4</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1039"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1040">4</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1041"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1042"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-128">
|
||
d((a_1, 1), (a_4, 4)) = d((a_1, 1), (a_2, 2)) + d((a_2, 2), (a_4, 4))
|
||
</script>
|
||
.
|
||
</p>
|
||
</div>
|
||
</div>
|
||
<p></p>
|
||
</div>
|
||
</div>
|
||
|
||
<script>
|
||
$(function () {
|
||
Codeforces.addMathJaxListener(function () {
|
||
let $problem = $('div[problemindex=C]')
|
||
let uuid = $problem.attr('data-uuid')
|
||
let statementText = convertStatementToText(
|
||
$problem.find('.ttypography').get(0)
|
||
)
|
||
|
||
let previousStatementText = Codeforces.getFromStorage(uuid)
|
||
if (previousStatementText) {
|
||
if (previousStatementText !== statementText) {
|
||
$problem.find('.diff-notifier').show()
|
||
|
||
$problem.find('.diff-notifier-close').click(function () {
|
||
Codeforces.putToStorageTtl(
|
||
uuid,
|
||
statementText,
|
||
6 * 60 * 60
|
||
)
|
||
$problem.find('.diff-notifier').hide()
|
||
})
|
||
|
||
$problem.find('a.view-changes').click(function () {
|
||
$.post(
|
||
'/data/diff',
|
||
{
|
||
action: 'getDiff',
|
||
a: previousStatementText,
|
||
b: statementText
|
||
},
|
||
function (result) {
|
||
if (result['success'] === 'true') {
|
||
Codeforces.facebox(
|
||
'.diff-popup',
|
||
'//codeforces.org/s/15523'
|
||
)
|
||
$('#facebox .diff-popup').html(result['diff'])
|
||
}
|
||
},
|
||
'json'
|
||
)
|
||
})
|
||
}
|
||
} else {
|
||
Codeforces.putToStorageTtl(uuid, statementText, 6 * 60 * 60)
|
||
}
|
||
})
|
||
})
|
||
</script>
|
||
<script type="text/javascript">
|
||
$(document).ready(function () {
|
||
const inputFileDiv = $('div.input-file')
|
||
const inputFile = inputFileDiv.text()
|
||
const outputFileDiv = $('div.output-file')
|
||
const outputFile = outputFileDiv.text()
|
||
|
||
if (
|
||
!endsWith(inputFile, 'standard input') &&
|
||
!endsWith(inputFile, 'standard input')
|
||
) {
|
||
inputFileDiv.attr('style', 'font-weight: bold')
|
||
}
|
||
|
||
if (
|
||
!endsWith(outputFile, 'standard output') &&
|
||
!endsWith(outputFile, 'standard output')
|
||
) {
|
||
outputFileDiv.attr('style', 'font-weight: bold')
|
||
}
|
||
|
||
const titleDiv = $('div.header div.title')
|
||
})
|
||
</script>
|
||
</div>
|
||
<div style="margin-bottom: 2em">
|
||
<div
|
||
class="problemindexholder"
|
||
problemindex="D"
|
||
data-uuid="ps_515ea55cc6ec3152039a89e81dba7559d15ff9d5"
|
||
>
|
||
<div
|
||
style="
|
||
display: none;
|
||
margin: 1em 0;
|
||
text-align: center;
|
||
position: relative;
|
||
"
|
||
class="alert alert-info diff-notifier"
|
||
>
|
||
<div>
|
||
The problem statement has recently been changed.
|
||
<a class="view-changes" href="#">View the changes.</a>
|
||
</div>
|
||
<span
|
||
class="diff-notifier-close"
|
||
style="
|
||
position: absolute;
|
||
top: 0.2em;
|
||
right: 0.3em;
|
||
cursor: pointer;
|
||
font-size: 1.4em;
|
||
"
|
||
>×</span
|
||
>
|
||
</div>
|
||
<div class="ttypography">
|
||
<div class="problem-statement">
|
||
<div class="header">
|
||
<div class="title">D. Excellent Arrays</div>
|
||
<div class="time-limit">
|
||
<div class="property-title">time limit per test</div>
|
||
2 seconds
|
||
</div>
|
||
<div class="memory-limit">
|
||
<div class="property-title">memory limit per test</div>
|
||
256 megabytes
|
||
</div>
|
||
<div class="input-file input-standard">
|
||
<div class="property-title">input</div>
|
||
standard input
|
||
</div>
|
||
<div class="output-file output-standard">
|
||
<div class="property-title">output</div>
|
||
standard output
|
||
</div>
|
||
</div>
|
||
<div>
|
||
<p>
|
||
Let's call an integer array
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1043"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1044"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1045"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-1046"
|
||
style="vertical-align: -0.4em"
|
||
>1</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1047"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1048"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1049"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-1050"
|
||
style="vertical-align: -0.4em"
|
||
>2</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1051"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1052"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>…</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1053"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1054"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1055"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-1056"
|
||
style="vertical-align: -0.4em"
|
||
>n</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-129">
|
||
a_1, a_2, \dots, a_n
|
||
</script>
|
||
<span class="tex-font-style-it">good</span> if
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1057"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1058"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1059"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-1060"
|
||
style="vertical-align: -0.4em"
|
||
>i</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1061"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≠</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1062"
|
||
>i</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-130">
|
||
a_i \neq i
|
||
</script>
|
||
for each
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1063"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1064"
|
||
>i</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-131">
|
||
i
|
||
</script>
|
||
.
|
||
</p>
|
||
<p>
|
||
Let
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1065"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1066"
|
||
>F</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1067"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1068"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1069"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-132">
|
||
F(a)
|
||
</script>
|
||
be the number of pairs
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1070"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1071"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1072"
|
||
>i</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1073"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1074"
|
||
>j</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1075"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-133">
|
||
(i, j)
|
||
</script>
|
||
(<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1076"
|
||
><span class="MJXp-mn" id="MJXp-Span-1077">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1078"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1079"
|
||
>i</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1080"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
><</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1081"
|
||
>j</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1082"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1083"
|
||
>n</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-134">
|
||
1 \le i < j \le n
|
||
</script>
|
||
) such that
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1084"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1085"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1086"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-1087"
|
||
style="vertical-align: -0.4em"
|
||
>i</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1088"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>+</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1089"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1090"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-1091"
|
||
style="vertical-align: -0.4em"
|
||
>j</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1092"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>=</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1093"
|
||
>i</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1094"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>+</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1095"
|
||
>j</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-135">
|
||
a_i + a_j = i + j
|
||
</script>
|
||
.
|
||
</p>
|
||
<p>
|
||
Let's say that an array
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1096"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1097"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1098"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-1099"
|
||
style="vertical-align: -0.4em"
|
||
>1</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1100"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1101"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1102"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-1103"
|
||
style="vertical-align: -0.4em"
|
||
>2</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1104"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1105"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>…</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1106"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1107"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1108"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-1109"
|
||
style="vertical-align: -0.4em"
|
||
>n</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-136">
|
||
a_1, a_2, \dots, a_n
|
||
</script>
|
||
is <span class="tex-font-style-it">excellent</span> if:
|
||
</p>
|
||
<ul>
|
||
<li>
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1110"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1111"
|
||
>a</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-137">
|
||
a
|
||
</script>
|
||
is <span class="tex-font-style-it">good</span>;
|
||
</li>
|
||
<li>
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1112"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1113"
|
||
>l</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1114"
|
||
style="
|
||
margin-left: 0.333em;
|
||
margin-right: 0.333em;
|
||
"
|
||
>≤</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1115"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1116"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-1117"
|
||
style="vertical-align: -0.4em"
|
||
>i</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1118"
|
||
style="
|
||
margin-left: 0.333em;
|
||
margin-right: 0.333em;
|
||
"
|
||
>≤</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1119"
|
||
>r</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-138">
|
||
l \le a_i \le r
|
||
</script>
|
||
for each
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1120"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1121"
|
||
>i</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-139">
|
||
i
|
||
</script>
|
||
;
|
||
</li>
|
||
<li>
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1122"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1123"
|
||
>F</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1124"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1125"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1126"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-140">
|
||
F(a)
|
||
</script>
|
||
is the maximum possible among all
|
||
<span class="tex-font-style-it">good</span> arrays of
|
||
size
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1127"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1128"
|
||
>n</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-141">
|
||
n
|
||
</script>
|
||
.
|
||
</li>
|
||
</ul>
|
||
<p>
|
||
Given
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1129"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1130"
|
||
>n</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-142">
|
||
n
|
||
</script>
|
||
,
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1131"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1132"
|
||
>l</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-143">
|
||
l
|
||
</script>
|
||
and
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1133"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1134"
|
||
>r</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-144">
|
||
r
|
||
</script>
|
||
, calculate the number of
|
||
<span class="tex-font-style-it">excellent</span> arrays
|
||
modulo
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1135"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1136"
|
||
><span
|
||
class="MJXp-mn"
|
||
id="MJXp-Span-1137"
|
||
style="margin-right: 0.05em"
|
||
>10</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-1138"
|
||
style="vertical-align: 0.5em"
|
||
>9</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1139"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>+</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1140"
|
||
>7</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-145">
|
||
10^9 + 7
|
||
</script>
|
||
.
|
||
</p>
|
||
</div>
|
||
<div class="input-specification">
|
||
<div class="section-title">Input</div>
|
||
<p>
|
||
The first line contains a single integer
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1141"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1142"
|
||
>t</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-146">
|
||
t
|
||
</script>
|
||
(<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1143"
|
||
><span class="MJXp-mn" id="MJXp-Span-1144">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1145"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1146"
|
||
>t</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1147"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1148"
|
||
>1000</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-147">
|
||
1 \le t \le 1000
|
||
</script>
|
||
) — the number of test cases.
|
||
</p>
|
||
<p>
|
||
The first and only line of each test case contains three
|
||
integers
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1149"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1150"
|
||
>n</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-148">
|
||
n
|
||
</script>
|
||
,
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1151"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1152"
|
||
>l</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-149">
|
||
l
|
||
</script>
|
||
, and
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1153"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1154"
|
||
>r</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-150">
|
||
r
|
||
</script>
|
||
(<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1155"
|
||
><span class="MJXp-mn" id="MJXp-Span-1156">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1157"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1158"
|
||
>n</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1159"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1160">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1161"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>⋅</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1162"
|
||
><span
|
||
class="MJXp-mn"
|
||
id="MJXp-Span-1163"
|
||
style="margin-right: 0.05em"
|
||
>10</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-1164"
|
||
style="vertical-align: 0.5em"
|
||
>5</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-151">
|
||
2 \le n \le 2 \cdot 10^5
|
||
</script>
|
||
;
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1165"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1166"
|
||
style="margin-left: 0em; margin-right: 0.111em"
|
||
>−</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1167"
|
||
><span
|
||
class="MJXp-mn"
|
||
id="MJXp-Span-1168"
|
||
style="margin-right: 0.05em"
|
||
>10</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-1169"
|
||
style="vertical-align: 0.5em"
|
||
>9</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1170"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1171"
|
||
>l</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1172"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1173"
|
||
>1</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-152">
|
||
-10^9 \le l \le 1
|
||
</script>
|
||
;
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1174"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1175"
|
||
>n</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1176"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1177"
|
||
>r</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1178"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1179"
|
||
><span
|
||
class="MJXp-mn"
|
||
id="MJXp-Span-1180"
|
||
style="margin-right: 0.05em"
|
||
>10</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-1181"
|
||
style="vertical-align: 0.5em"
|
||
>9</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-153">
|
||
n \le r \le 10^9
|
||
</script>
|
||
).
|
||
</p>
|
||
<p>
|
||
It's guaranteed that the sum of
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1182"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1183"
|
||
>n</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-154">
|
||
n
|
||
</script>
|
||
doesn't exceed
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1184"
|
||
><span class="MJXp-mn" id="MJXp-Span-1185">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1186"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>⋅</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1187"
|
||
><span
|
||
class="MJXp-mn"
|
||
id="MJXp-Span-1188"
|
||
style="margin-right: 0.05em"
|
||
>10</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-1189"
|
||
style="vertical-align: 0.5em"
|
||
>5</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-155">
|
||
2 \cdot 10^5
|
||
</script>
|
||
.
|
||
</p>
|
||
</div>
|
||
<div class="output-specification">
|
||
<div class="section-title">Output</div>
|
||
<p>
|
||
For each test case, print the number of excellent arrays
|
||
modulo
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1190"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1191"
|
||
><span
|
||
class="MJXp-mn"
|
||
id="MJXp-Span-1192"
|
||
style="margin-right: 0.05em"
|
||
>10</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-1193"
|
||
style="vertical-align: 0.5em"
|
||
>9</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1194"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>+</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1195"
|
||
>7</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-156">
|
||
10^9 + 7
|
||
</script>
|
||
.
|
||
</p>
|
||
</div>
|
||
<div class="sample-tests">
|
||
<div class="section-title">Example</div>
|
||
<div class="sample-test">
|
||
<div class="input">
|
||
<div class="title">
|
||
Input
|
||
<div
|
||
title="Copy"
|
||
data-clipboard-target="#id0023043713167808821"
|
||
id="id004407875898011011"
|
||
class="input-output-copier"
|
||
>
|
||
Copy
|
||
</div>
|
||
</div>
|
||
<pre id="id0023043713167808821">
|
||
4
|
||
3 0 3
|
||
4 -3 5
|
||
42 -33 55
|
||
69 -42 146
|
||
</pre
|
||
>
|
||
</div>
|
||
<div class="output">
|
||
<div class="title">
|
||
Output
|
||
<div
|
||
title="Copy"
|
||
data-clipboard-target="#id004542568812571498"
|
||
id="id008244354808710753"
|
||
class="input-output-copier"
|
||
>
|
||
Copy
|
||
</div>
|
||
</div>
|
||
<pre id="id004542568812571498">
|
||
4
|
||
10
|
||
143922563
|
||
698570404
|
||
</pre
|
||
>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<div class="note">
|
||
<div class="section-title">Note</div>
|
||
<p>
|
||
In the first test case, it can be proven that the maximum
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1196"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1197"
|
||
>F</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1198"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>(</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1199"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1200"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>)</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-157">
|
||
F(a)
|
||
</script>
|
||
among all
|
||
<span class="tex-font-style-it">good</span> arrays
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1201"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1202"
|
||
>a</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-158">
|
||
a
|
||
</script>
|
||
is equal to
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1203"
|
||
><span class="MJXp-mn" id="MJXp-Span-1204"
|
||
>2</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-159">
|
||
2
|
||
</script>
|
||
. The excellent arrays are:
|
||
</p>
|
||
<ol>
|
||
<li>
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1205"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1206"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>[</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1207">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1208"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1209">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1210"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1211">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1212"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>]</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-160">
|
||
[2, 1, 2]
|
||
</script>
|
||
;
|
||
</li>
|
||
<li>
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1213"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1214"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>[</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1215">0</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1216"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1217">3</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1218"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1219">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1220"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>]</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-161">
|
||
[0, 3, 2]
|
||
</script>
|
||
;
|
||
</li>
|
||
<li>
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1221"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1222"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>[</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1223">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1224"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1225">3</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1226"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1227">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1228"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>]</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-162">
|
||
[2, 3, 2]
|
||
</script>
|
||
;
|
||
</li>
|
||
<li>
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1229"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1230"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>[</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1231">3</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1232"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1233">0</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1234"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1235">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1236"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>]</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-163">
|
||
[3, 0, 1]
|
||
</script>
|
||
.
|
||
</li>
|
||
</ol>
|
||
</div>
|
||
</div>
|
||
<p></p>
|
||
</div>
|
||
</div>
|
||
|
||
<script>
|
||
$(function () {
|
||
Codeforces.addMathJaxListener(function () {
|
||
let $problem = $('div[problemindex=D]')
|
||
let uuid = $problem.attr('data-uuid')
|
||
let statementText = convertStatementToText(
|
||
$problem.find('.ttypography').get(0)
|
||
)
|
||
|
||
let previousStatementText = Codeforces.getFromStorage(uuid)
|
||
if (previousStatementText) {
|
||
if (previousStatementText !== statementText) {
|
||
$problem.find('.diff-notifier').show()
|
||
|
||
$problem.find('.diff-notifier-close').click(function () {
|
||
Codeforces.putToStorageTtl(
|
||
uuid,
|
||
statementText,
|
||
6 * 60 * 60
|
||
)
|
||
$problem.find('.diff-notifier').hide()
|
||
})
|
||
|
||
$problem.find('a.view-changes').click(function () {
|
||
$.post(
|
||
'/data/diff',
|
||
{
|
||
action: 'getDiff',
|
||
a: previousStatementText,
|
||
b: statementText
|
||
},
|
||
function (result) {
|
||
if (result['success'] === 'true') {
|
||
Codeforces.facebox(
|
||
'.diff-popup',
|
||
'//codeforces.org/s/15523'
|
||
)
|
||
$('#facebox .diff-popup').html(result['diff'])
|
||
}
|
||
},
|
||
'json'
|
||
)
|
||
})
|
||
}
|
||
} else {
|
||
Codeforces.putToStorageTtl(uuid, statementText, 6 * 60 * 60)
|
||
}
|
||
})
|
||
})
|
||
</script>
|
||
<script type="text/javascript">
|
||
$(document).ready(function () {
|
||
const inputFileDiv = $('div.input-file')
|
||
const inputFile = inputFileDiv.text()
|
||
const outputFileDiv = $('div.output-file')
|
||
const outputFile = outputFileDiv.text()
|
||
|
||
if (
|
||
!endsWith(inputFile, 'standard input') &&
|
||
!endsWith(inputFile, 'standard input')
|
||
) {
|
||
inputFileDiv.attr('style', 'font-weight: bold')
|
||
}
|
||
|
||
if (
|
||
!endsWith(outputFile, 'standard output') &&
|
||
!endsWith(outputFile, 'standard output')
|
||
) {
|
||
outputFileDiv.attr('style', 'font-weight: bold')
|
||
}
|
||
|
||
const titleDiv = $('div.header div.title')
|
||
})
|
||
</script>
|
||
</div>
|
||
<div style="margin-bottom: 2em">
|
||
<div
|
||
class="problemindexholder"
|
||
problemindex="E"
|
||
data-uuid="ps_dd28f1f2ac52ae740b63aee0f0cf48df0cf99ac3"
|
||
>
|
||
<div
|
||
style="
|
||
display: none;
|
||
margin: 1em 0;
|
||
text-align: center;
|
||
position: relative;
|
||
"
|
||
class="alert alert-info diff-notifier"
|
||
>
|
||
<div>
|
||
The problem statement has recently been changed.
|
||
<a class="view-changes" href="#">View the changes.</a>
|
||
</div>
|
||
<span
|
||
class="diff-notifier-close"
|
||
style="
|
||
position: absolute;
|
||
top: 0.2em;
|
||
right: 0.3em;
|
||
cursor: pointer;
|
||
font-size: 1.4em;
|
||
"
|
||
>×</span
|
||
>
|
||
</div>
|
||
<div class="ttypography">
|
||
<div class="problem-statement">
|
||
<div class="header">
|
||
<div class="title">E. Stringforces</div>
|
||
<div class="time-limit">
|
||
<div class="property-title">time limit per test</div>
|
||
3 seconds
|
||
</div>
|
||
<div class="memory-limit">
|
||
<div class="property-title">memory limit per test</div>
|
||
256 megabytes
|
||
</div>
|
||
<div class="input-file input-standard">
|
||
<div class="property-title">input</div>
|
||
standard input
|
||
</div>
|
||
<div class="output-file output-standard">
|
||
<div class="property-title">output</div>
|
||
standard output
|
||
</div>
|
||
</div>
|
||
<div>
|
||
<p>
|
||
You are given a string
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1237"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1238"
|
||
>s</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-164">
|
||
s
|
||
</script>
|
||
of length
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1239"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1240"
|
||
>n</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-165">
|
||
n
|
||
</script>
|
||
. Each character is either one of the first
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1241"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1242"
|
||
>k</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-166">
|
||
k
|
||
</script>
|
||
lowercase Latin letters or a question mark.
|
||
</p>
|
||
<p>
|
||
You are asked to replace every question mark with one of
|
||
the first
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1243"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1244"
|
||
>k</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-167">
|
||
k
|
||
</script>
|
||
lowercase Latin letters in such a way that the following
|
||
value is maximized.
|
||
</p>
|
||
<p>
|
||
Let
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1245"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1246"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1247"
|
||
style="margin-right: 0.05em"
|
||
>f</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-1248"
|
||
style="vertical-align: -0.4em"
|
||
>i</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-168">
|
||
f_i
|
||
</script>
|
||
be the maximum length substring of string
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1249"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1250"
|
||
>s</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-169">
|
||
s
|
||
</script>
|
||
, which consists entirely of the
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1251"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1252"
|
||
>i</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-170">
|
||
i
|
||
</script>
|
||
-th Latin letter. A substring of a string is a contiguous
|
||
subsequence of that string. If the
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1253"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1254"
|
||
>i</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-171">
|
||
i
|
||
</script>
|
||
-th letter doesn't appear in a string, then
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1255"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1256"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1257"
|
||
style="margin-right: 0.05em"
|
||
>f</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-1258"
|
||
style="vertical-align: -0.4em"
|
||
>i</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-172">
|
||
f_i
|
||
</script>
|
||
is equal to
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1259"
|
||
><span class="MJXp-mn" id="MJXp-Span-1260"
|
||
>0</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-173">
|
||
0
|
||
</script>
|
||
.
|
||
</p>
|
||
<p>
|
||
The value of a string
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1261"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1262"
|
||
>s</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-174">
|
||
s
|
||
</script>
|
||
is the minimum value among
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1263"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1264"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1265"
|
||
style="margin-right: 0.05em"
|
||
>f</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-1266"
|
||
style="vertical-align: -0.4em"
|
||
>i</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-175">
|
||
f_i
|
||
</script>
|
||
for all
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1267"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1268"
|
||
>i</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-176">
|
||
i
|
||
</script>
|
||
from
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1269"
|
||
><span class="MJXp-mn" id="MJXp-Span-1270"
|
||
>1</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-177">
|
||
1
|
||
</script>
|
||
to
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1271"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1272"
|
||
>k</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-178">
|
||
k
|
||
</script>
|
||
.
|
||
</p>
|
||
<p>What is the maximum value the string can have?</p>
|
||
</div>
|
||
<div class="input-specification">
|
||
<div class="section-title">Input</div>
|
||
<p>
|
||
The first line contains two integers
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1273"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1274"
|
||
>n</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-179">
|
||
n
|
||
</script>
|
||
and
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1275"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1276"
|
||
>k</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-180">
|
||
k
|
||
</script>
|
||
(<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1277"
|
||
><span class="MJXp-mn" id="MJXp-Span-1278">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1279"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1280"
|
||
>n</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1281"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1282">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1283"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>⋅</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1284"
|
||
><span
|
||
class="MJXp-mn"
|
||
id="MJXp-Span-1285"
|
||
style="margin-right: 0.05em"
|
||
>10</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-1286"
|
||
style="vertical-align: 0.5em"
|
||
>5</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-181">
|
||
1 \le n \le 2 \cdot 10^5
|
||
</script>
|
||
;
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1287"
|
||
><span class="MJXp-mn" id="MJXp-Span-1288">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1289"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1290"
|
||
>k</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1291"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1292"
|
||
>17</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-182">
|
||
1 \le k \le 17
|
||
</script>
|
||
) — the length of the string and the number of first Latin
|
||
letters used.
|
||
</p>
|
||
<p>
|
||
The second line contains a string
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1293"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1294"
|
||
>s</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-183">
|
||
s
|
||
</script>
|
||
, consisting of
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1295"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1296"
|
||
>n</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-184">
|
||
n
|
||
</script>
|
||
characters. Each character is either one of the first
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1297"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1298"
|
||
>k</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-185">
|
||
k
|
||
</script>
|
||
lowercase Latin letters or a question mark.
|
||
</p>
|
||
</div>
|
||
<div class="output-specification">
|
||
<div class="section-title">Output</div>
|
||
<p>
|
||
Print a single integer — the maximum value of the string
|
||
after every question mark is replaced with one of the
|
||
first
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1299"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1300"
|
||
>k</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-186">
|
||
k
|
||
</script>
|
||
lowercase Latin letters.
|
||
</p>
|
||
</div>
|
||
<div class="sample-tests">
|
||
<div class="section-title">Examples</div>
|
||
<div class="sample-test">
|
||
<div class="input">
|
||
<div class="title">
|
||
Input
|
||
<div
|
||
title="Copy"
|
||
data-clipboard-target="#id0010278017840988773"
|
||
id="id0036697665286741366"
|
||
class="input-output-copier"
|
||
>
|
||
Copy
|
||
</div>
|
||
</div>
|
||
<pre id="id0010278017840988773">
|
||
10 2
|
||
a??ab????b
|
||
</pre
|
||
>
|
||
</div>
|
||
<div class="output">
|
||
<div class="title">
|
||
Output
|
||
<div
|
||
title="Copy"
|
||
data-clipboard-target="#id0012852910736247602"
|
||
id="id0023007378841179338"
|
||
class="input-output-copier"
|
||
>
|
||
Copy
|
||
</div>
|
||
</div>
|
||
<pre id="id0012852910736247602">
|
||
4
|
||
</pre
|
||
>
|
||
</div>
|
||
<div class="input">
|
||
<div class="title">
|
||
Input
|
||
<div
|
||
title="Copy"
|
||
data-clipboard-target="#id008360522336769922"
|
||
id="id006567512747417346"
|
||
class="input-output-copier"
|
||
>
|
||
Copy
|
||
</div>
|
||
</div>
|
||
<pre id="id008360522336769922">
|
||
9 4
|
||
?????????
|
||
</pre
|
||
>
|
||
</div>
|
||
<div class="output">
|
||
<div class="title">
|
||
Output
|
||
<div
|
||
title="Copy"
|
||
data-clipboard-target="#id003666838310571824"
|
||
id="id007490701155756769"
|
||
class="input-output-copier"
|
||
>
|
||
Copy
|
||
</div>
|
||
</div>
|
||
<pre id="id003666838310571824">
|
||
2
|
||
</pre
|
||
>
|
||
</div>
|
||
<div class="input">
|
||
<div class="title">
|
||
Input
|
||
<div
|
||
title="Copy"
|
||
data-clipboard-target="#id004808096454233227"
|
||
id="id0029136739482146945"
|
||
class="input-output-copier"
|
||
>
|
||
Copy
|
||
</div>
|
||
</div>
|
||
<pre id="id004808096454233227">
|
||
2 3
|
||
??
|
||
</pre
|
||
>
|
||
</div>
|
||
<div class="output">
|
||
<div class="title">
|
||
Output
|
||
<div
|
||
title="Copy"
|
||
data-clipboard-target="#id0020261251752636744"
|
||
id="id008323933857992657"
|
||
class="input-output-copier"
|
||
>
|
||
Copy
|
||
</div>
|
||
</div>
|
||
<pre id="id0020261251752636744">
|
||
0
|
||
</pre
|
||
>
|
||
</div>
|
||
<div class="input">
|
||
<div class="title">
|
||
Input
|
||
<div
|
||
title="Copy"
|
||
data-clipboard-target="#id006719335306102051"
|
||
id="id007729559272990804"
|
||
class="input-output-copier"
|
||
>
|
||
Copy
|
||
</div>
|
||
</div>
|
||
<pre id="id006719335306102051">
|
||
15 3
|
||
??b?babbc??b?aa
|
||
</pre
|
||
>
|
||
</div>
|
||
<div class="output">
|
||
<div class="title">
|
||
Output
|
||
<div
|
||
title="Copy"
|
||
data-clipboard-target="#id0011681461962729234"
|
||
id="id005737182969104904"
|
||
class="input-output-copier"
|
||
>
|
||
Copy
|
||
</div>
|
||
</div>
|
||
<pre id="id0011681461962729234">
|
||
3
|
||
</pre
|
||
>
|
||
</div>
|
||
<div class="input">
|
||
<div class="title">
|
||
Input
|
||
<div
|
||
title="Copy"
|
||
data-clipboard-target="#id0049861046124584174"
|
||
id="id00027302885836351765"
|
||
class="input-output-copier"
|
||
>
|
||
Copy
|
||
</div>
|
||
</div>
|
||
<pre id="id0049861046124584174">
|
||
4 4
|
||
cabd
|
||
</pre
|
||
>
|
||
</div>
|
||
<div class="output">
|
||
<div class="title">
|
||
Output
|
||
<div
|
||
title="Copy"
|
||
data-clipboard-target="#id007620779631950757"
|
||
id="id00005901348145114671"
|
||
class="input-output-copier"
|
||
>
|
||
Copy
|
||
</div>
|
||
</div>
|
||
<pre id="id007620779631950757">
|
||
1
|
||
</pre
|
||
>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<div class="note">
|
||
<div class="section-title">Note</div>
|
||
<p>
|
||
In the first example the question marks can be replaced in
|
||
the following way: "<span class="tex-font-style-tt"
|
||
>a<span class="tex-font-style-underline">aa</span
|
||
>ab<span class="tex-font-style-underline">abbb</span
|
||
>b</span
|
||
>".
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1301"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1302"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1303"
|
||
style="margin-right: 0.05em"
|
||
>f</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-1304"
|
||
style="vertical-align: -0.4em"
|
||
>1</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1305"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>=</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1306"
|
||
>4</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-187">
|
||
f_1 = 4
|
||
</script>
|
||
,
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1307"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1308"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1309"
|
||
style="margin-right: 0.05em"
|
||
>f</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-1310"
|
||
style="vertical-align: -0.4em"
|
||
>2</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1311"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>=</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1312"
|
||
>4</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-188">
|
||
f_2 = 4
|
||
</script>
|
||
, thus the answer is
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1313"
|
||
><span class="MJXp-mn" id="MJXp-Span-1314"
|
||
>4</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-189">
|
||
4
|
||
</script>
|
||
. Replacing it like this is also possible: "<span
|
||
class="tex-font-style-tt"
|
||
>a<span class="tex-font-style-underline">aa</span
|
||
>ab<span class="tex-font-style-underline">bbbb</span
|
||
>b</span
|
||
>". That way
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1315"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1316"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1317"
|
||
style="margin-right: 0.05em"
|
||
>f</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-1318"
|
||
style="vertical-align: -0.4em"
|
||
>1</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1319"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>=</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1320"
|
||
>4</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-190">
|
||
f_1 = 4
|
||
</script>
|
||
,
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1321"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1322"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1323"
|
||
style="margin-right: 0.05em"
|
||
>f</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-1324"
|
||
style="vertical-align: -0.4em"
|
||
>2</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1325"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>=</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1326"
|
||
>6</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-191">
|
||
f_2 = 6
|
||
</script>
|
||
, however, the minimum of them is still
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1327"
|
||
><span class="MJXp-mn" id="MJXp-Span-1328"
|
||
>4</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-192">
|
||
4
|
||
</script>
|
||
.
|
||
</p>
|
||
<p>
|
||
In the second example one of the possible strings is
|
||
"<span class="tex-font-style-tt"
|
||
><span class="tex-font-style-underline"
|
||
>aabbccdda</span
|
||
></span
|
||
>".
|
||
</p>
|
||
<p>
|
||
In the third example at least one letter won't appear in
|
||
the string, thus, the minimum of values
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1329"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1330"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1331"
|
||
style="margin-right: 0.05em"
|
||
>f</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-1332"
|
||
style="vertical-align: -0.4em"
|
||
>i</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-193">
|
||
f_i
|
||
</script>
|
||
is always
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1333"
|
||
><span class="MJXp-mn" id="MJXp-Span-1334"
|
||
>0</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-194">
|
||
0
|
||
</script>
|
||
.
|
||
</p>
|
||
</div>
|
||
</div>
|
||
<p></p>
|
||
</div>
|
||
</div>
|
||
|
||
<script>
|
||
$(function () {
|
||
Codeforces.addMathJaxListener(function () {
|
||
let $problem = $('div[problemindex=E]')
|
||
let uuid = $problem.attr('data-uuid')
|
||
let statementText = convertStatementToText(
|
||
$problem.find('.ttypography').get(0)
|
||
)
|
||
|
||
let previousStatementText = Codeforces.getFromStorage(uuid)
|
||
if (previousStatementText) {
|
||
if (previousStatementText !== statementText) {
|
||
$problem.find('.diff-notifier').show()
|
||
|
||
$problem.find('.diff-notifier-close').click(function () {
|
||
Codeforces.putToStorageTtl(
|
||
uuid,
|
||
statementText,
|
||
6 * 60 * 60
|
||
)
|
||
$problem.find('.diff-notifier').hide()
|
||
})
|
||
|
||
$problem.find('a.view-changes').click(function () {
|
||
$.post(
|
||
'/data/diff',
|
||
{
|
||
action: 'getDiff',
|
||
a: previousStatementText,
|
||
b: statementText
|
||
},
|
||
function (result) {
|
||
if (result['success'] === 'true') {
|
||
Codeforces.facebox(
|
||
'.diff-popup',
|
||
'//codeforces.org/s/15523'
|
||
)
|
||
$('#facebox .diff-popup').html(result['diff'])
|
||
}
|
||
},
|
||
'json'
|
||
)
|
||
})
|
||
}
|
||
} else {
|
||
Codeforces.putToStorageTtl(uuid, statementText, 6 * 60 * 60)
|
||
}
|
||
})
|
||
})
|
||
</script>
|
||
<script type="text/javascript">
|
||
$(document).ready(function () {
|
||
const inputFileDiv = $('div.input-file')
|
||
const inputFile = inputFileDiv.text()
|
||
const outputFileDiv = $('div.output-file')
|
||
const outputFile = outputFileDiv.text()
|
||
|
||
if (
|
||
!endsWith(inputFile, 'standard input') &&
|
||
!endsWith(inputFile, 'standard input')
|
||
) {
|
||
inputFileDiv.attr('style', 'font-weight: bold')
|
||
}
|
||
|
||
if (
|
||
!endsWith(outputFile, 'standard output') &&
|
||
!endsWith(outputFile, 'standard output')
|
||
) {
|
||
outputFileDiv.attr('style', 'font-weight: bold')
|
||
}
|
||
|
||
const titleDiv = $('div.header div.title')
|
||
})
|
||
</script>
|
||
</div>
|
||
<div style="margin-bottom: 1em">
|
||
<div
|
||
class="problemindexholder"
|
||
problemindex="F"
|
||
data-uuid="ps_0f51dc10ae570758a4dd7be335e4001d92c15179"
|
||
>
|
||
<div
|
||
style="
|
||
display: none;
|
||
margin: 1em 0;
|
||
text-align: center;
|
||
position: relative;
|
||
"
|
||
class="alert alert-info diff-notifier"
|
||
>
|
||
<div>
|
||
The problem statement has recently been changed.
|
||
<a class="view-changes" href="#">View the changes.</a>
|
||
</div>
|
||
<span
|
||
class="diff-notifier-close"
|
||
style="
|
||
position: absolute;
|
||
top: 0.2em;
|
||
right: 0.3em;
|
||
cursor: pointer;
|
||
font-size: 1.4em;
|
||
"
|
||
>×</span
|
||
>
|
||
</div>
|
||
<div class="ttypography">
|
||
<div class="problem-statement">
|
||
<div class="header">
|
||
<div class="title">F. Jumping Around</div>
|
||
<div class="time-limit">
|
||
<div class="property-title">time limit per test</div>
|
||
5 seconds
|
||
</div>
|
||
<div class="memory-limit">
|
||
<div class="property-title">memory limit per test</div>
|
||
256 megabytes
|
||
</div>
|
||
<div class="input-file input-standard">
|
||
<div class="property-title">input</div>
|
||
standard input
|
||
</div>
|
||
<div class="output-file output-standard">
|
||
<div class="property-title">output</div>
|
||
standard output
|
||
</div>
|
||
</div>
|
||
<div>
|
||
<p>
|
||
There is an infinite pond that can be represented with a
|
||
number line. There are
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1335"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1336"
|
||
>n</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-195">
|
||
n
|
||
</script>
|
||
rocks in the pond, numbered from
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1337"
|
||
><span class="MJXp-mn" id="MJXp-Span-1338"
|
||
>1</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-196">
|
||
1
|
||
</script>
|
||
to
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1339"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1340"
|
||
>n</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-197">
|
||
n
|
||
</script>
|
||
. The
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1341"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1342"
|
||
>i</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-198">
|
||
i
|
||
</script>
|
||
-th rock is located at an integer coordinate
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1343"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1344"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1345"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-1346"
|
||
style="vertical-align: -0.4em"
|
||
>i</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-199">
|
||
a_i
|
||
</script>
|
||
. The coordinates of the rocks are pairwise distinct. The
|
||
rocks are numbered in the increasing order of the
|
||
coordinate, so
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1347"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1348"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1349"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-1350"
|
||
style="vertical-align: -0.4em"
|
||
>1</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1351"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
><</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1352"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1353"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-1354"
|
||
style="vertical-align: -0.4em"
|
||
>2</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1355"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
><</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1356"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>⋯</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1357"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
><</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1358"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1359"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-1360"
|
||
style="vertical-align: -0.4em"
|
||
>n</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-200">
|
||
a_1 < a_2 < \dots < a_n
|
||
</script>
|
||
.
|
||
</p>
|
||
<p>
|
||
A robot frog sits on the rock number
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1361"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1362"
|
||
>s</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-201">
|
||
s
|
||
</script>
|
||
. The frog is programmable. It has a base jumping distance
|
||
parameter
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1363"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1364"
|
||
>d</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-202">
|
||
d
|
||
</script>
|
||
. There also is a setting for the jumping distance range.
|
||
If the jumping distance range is set to some integer
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1365"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1366"
|
||
>k</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-203">
|
||
k
|
||
</script>
|
||
, then the frog can jump from some rock to any rock at a
|
||
distance from
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1367"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1368"
|
||
>d</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1369"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>−</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1370"
|
||
>k</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-204">
|
||
d - k
|
||
</script>
|
||
to
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1371"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1372"
|
||
>d</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1373"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>+</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1374"
|
||
>k</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-205">
|
||
d + k
|
||
</script>
|
||
inclusive in any direction. The distance between two rocks
|
||
is an absolute difference between their coordinates.
|
||
</p>
|
||
<p>
|
||
You are assigned a task to implement a feature for the
|
||
frog. Given two integers
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1375"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1376"
|
||
>i</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-206">
|
||
i
|
||
</script>
|
||
and
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1377"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1378"
|
||
>k</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-207">
|
||
k
|
||
</script>
|
||
determine if the frog can reach a rock number
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1379"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1380"
|
||
>i</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-208">
|
||
i
|
||
</script>
|
||
from a rock number
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1381"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1382"
|
||
>s</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-209">
|
||
s
|
||
</script>
|
||
performing a sequence of jumps with the jumping distance
|
||
range set to
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1383"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1384"
|
||
>k</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-210">
|
||
k
|
||
</script>
|
||
. The sequence can be arbitrarily long or empty.
|
||
</p>
|
||
<p>
|
||
You will be given
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1385"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1386"
|
||
>q</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-211">
|
||
q
|
||
</script>
|
||
testcases for that feature, the
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1387"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1388"
|
||
>j</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-212">
|
||
j
|
||
</script>
|
||
-th testcase consists of two integers
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1389"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1390"
|
||
>i</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-213">
|
||
i
|
||
</script>
|
||
and
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1391"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1392"
|
||
>k</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-214">
|
||
k
|
||
</script>
|
||
. Print "<span class="tex-font-style-tt">Yes</span>" if
|
||
the
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1393"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1394"
|
||
>i</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-215">
|
||
i
|
||
</script>
|
||
-th rock is reachable and "<span class="tex-font-style-tt"
|
||
>No</span
|
||
>" otherwise.
|
||
</p>
|
||
<p>
|
||
You can output "<span class="tex-font-style-tt">YES</span
|
||
>" and "<span class="tex-font-style-tt">NO</span>" in any
|
||
case (for example, strings "<span
|
||
class="tex-font-style-tt"
|
||
>yEs</span
|
||
>", "<span class="tex-font-style-tt">yes</span>", "<span
|
||
class="tex-font-style-tt"
|
||
>Yes</span
|
||
>" and '<span class="tex-font-style-tt">YES</span>"' will
|
||
be recognized as a positive answer).
|
||
</p>
|
||
</div>
|
||
<div class="input-specification">
|
||
<div class="section-title">Input</div>
|
||
<p>
|
||
The first line contains four integers
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1395"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1396"
|
||
>n</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-216">
|
||
n
|
||
</script>
|
||
,
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1397"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1398"
|
||
>q</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-217">
|
||
q
|
||
</script>
|
||
,
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1399"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1400"
|
||
>s</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-218">
|
||
s
|
||
</script>
|
||
and
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1401"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1402"
|
||
>d</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-219">
|
||
d
|
||
</script>
|
||
(<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1403"
|
||
><span class="MJXp-mn" id="MJXp-Span-1404">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1405"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1406"
|
||
>n</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1407"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1408"
|
||
>q</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1409"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1410">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1411"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>⋅</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1412"
|
||
><span
|
||
class="MJXp-mn"
|
||
id="MJXp-Span-1413"
|
||
style="margin-right: 0.05em"
|
||
>10</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-1414"
|
||
style="vertical-align: 0.5em"
|
||
>5</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-220">
|
||
1 \le n, q \le 2 \cdot 10^5
|
||
</script>
|
||
;
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1415"
|
||
><span class="MJXp-mn" id="MJXp-Span-1416">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1417"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1418"
|
||
>s</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1419"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1420"
|
||
>n</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-221">
|
||
1 \le s \le n
|
||
</script>
|
||
;
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1421"
|
||
><span class="MJXp-mn" id="MJXp-Span-1422">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1423"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1424"
|
||
>d</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1425"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1426"
|
||
><span
|
||
class="MJXp-mn"
|
||
id="MJXp-Span-1427"
|
||
style="margin-right: 0.05em"
|
||
>10</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-1428"
|
||
style="vertical-align: 0.5em"
|
||
>6</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-222">
|
||
1 \le d \le 10^6
|
||
</script>
|
||
) — the number of rocks, the number of testcases, the
|
||
starting rock and the base jumping distance parameter.
|
||
</p>
|
||
<p>
|
||
The second line contains
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1429"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1430"
|
||
>n</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-223">
|
||
n
|
||
</script>
|
||
integers
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1431"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1432"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1433"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-1434"
|
||
style="vertical-align: -0.4em"
|
||
>1</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1435"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1436"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1437"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-1438"
|
||
style="vertical-align: -0.4em"
|
||
>2</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1439"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1440"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>…</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1441"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>,</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1442"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1443"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-1444"
|
||
style="vertical-align: -0.4em"
|
||
>n</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-224">
|
||
a_1, a_2, \dots, a_n
|
||
</script>
|
||
(<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1445"
|
||
><span class="MJXp-mn" id="MJXp-Span-1446">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1447"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1448"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1449"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-1450"
|
||
style="vertical-align: -0.4em"
|
||
>i</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1451"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1452"
|
||
><span
|
||
class="MJXp-mn"
|
||
id="MJXp-Span-1453"
|
||
style="margin-right: 0.05em"
|
||
>10</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-1454"
|
||
style="vertical-align: 0.5em"
|
||
>6</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-225">
|
||
1 \le a_i \le 10^6
|
||
</script>
|
||
) — the coordinates of the rocks. The coordinates of the
|
||
rocks are pairwise distinct. The rocks are numbered in the
|
||
increasing order of distance from the land, so
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1455"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1456"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1457"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-1458"
|
||
style="vertical-align: -0.4em"
|
||
>1</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1459"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
><</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1460"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1461"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-1462"
|
||
style="vertical-align: -0.4em"
|
||
>2</span
|
||
></span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1463"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
><</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1464"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>⋯</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1465"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
><</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1466"
|
||
><span
|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-1467"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
><span
|
||
class="MJXp-mi MJXp-italic MJXp-script"
|
||
id="MJXp-Span-1468"
|
||
style="vertical-align: -0.4em"
|
||
>n</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-226">
|
||
a_1 < a_2 < \dots < a_n
|
||
</script>
|
||
.
|
||
</p>
|
||
<p>
|
||
Each of the next
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1469"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1470"
|
||
>q</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-227">
|
||
q
|
||
</script>
|
||
lines contains two integers
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1471"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1472"
|
||
>i</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-228">
|
||
i
|
||
</script>
|
||
and
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1473"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1474"
|
||
>k</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-229">
|
||
k
|
||
</script>
|
||
(<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1475"
|
||
><span class="MJXp-mn" id="MJXp-Span-1476">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1477"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1478"
|
||
>i</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1479"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1480"
|
||
>n</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-230">
|
||
1 \le i \le n
|
||
</script>
|
||
;
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1481"
|
||
><span class="MJXp-mn" id="MJXp-Span-1482">1</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1483"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1484"
|
||
>k</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1485"
|
||
style="margin-left: 0.333em; margin-right: 0.333em"
|
||
>≤</span
|
||
><span class="MJXp-msubsup" id="MJXp-Span-1486"
|
||
><span
|
||
class="MJXp-mn"
|
||
id="MJXp-Span-1487"
|
||
style="margin-right: 0.05em"
|
||
>10</span
|
||
><span
|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-1488"
|
||
style="vertical-align: 0.5em"
|
||
>6</span
|
||
></span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-231">
|
||
1 \le k \le 10^6
|
||
</script>
|
||
) — the parameters to the testcase.
|
||
</p>
|
||
</div>
|
||
<div class="output-specification">
|
||
<div class="section-title">Output</div>
|
||
<p>
|
||
For each of the testcases print an answer. If there is a
|
||
sequence of jumps from a rock number
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1489"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1490"
|
||
>s</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-232">
|
||
s
|
||
</script>
|
||
to a rock number
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1491"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1492"
|
||
>i</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-233">
|
||
i
|
||
</script>
|
||
with the jumping distance range set to
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1493"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-1494"
|
||
>k</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-234">
|
||
k
|
||
</script>
|
||
, then print "<span class="tex-font-style-tt">Yes</span>".
|
||
Otherwise, print "<span class="tex-font-style-tt">No</span
|
||
>".
|
||
</p>
|
||
</div>
|
||
<div class="sample-tests">
|
||
<div class="section-title">Examples</div>
|
||
<div class="sample-test">
|
||
<div class="input">
|
||
<div class="title">
|
||
Input
|
||
<div
|
||
title="Copy"
|
||
data-clipboard-target="#id009457268175320975"
|
||
id="id0009232387181386903"
|
||
class="input-output-copier"
|
||
>
|
||
Copy
|
||
</div>
|
||
</div>
|
||
<pre id="id009457268175320975">
|
||
7 4 4 5
|
||
1 5 10 13 20 22 28
|
||
4 1
|
||
7 2
|
||
7 3
|
||
3 2
|
||
</pre
|
||
>
|
||
</div>
|
||
<div class="output">
|
||
<div class="title">
|
||
Output
|
||
<div
|
||
title="Copy"
|
||
data-clipboard-target="#id006703894185413486"
|
||
id="id009325666133454178"
|
||
class="input-output-copier"
|
||
>
|
||
Copy
|
||
</div>
|
||
</div>
|
||
<pre id="id006703894185413486">
|
||
Yes
|
||
No
|
||
Yes
|
||
Yes
|
||
</pre
|
||
>
|
||
</div>
|
||
<div class="input">
|
||
<div class="title">
|
||
Input
|
||
<div
|
||
title="Copy"
|
||
data-clipboard-target="#id003030451618641431"
|
||
id="id0012268541365229912"
|
||
class="input-output-copier"
|
||
>
|
||
Copy
|
||
</div>
|
||
</div>
|
||
<pre id="id003030451618641431">
|
||
10 8 6 11
|
||
1 2 4 7 8 9 11 13 19 20
|
||
2 13
|
||
5 8
|
||
8 1
|
||
6 15
|
||
1 15
|
||
2 7
|
||
7 6
|
||
8 9
|
||
</pre
|
||
>
|
||
</div>
|
||
<div class="output">
|
||
<div class="title">
|
||
Output
|
||
<div
|
||
title="Copy"
|
||
data-clipboard-target="#id00007163596982270759"
|
||
id="id0004696282416006514"
|
||
class="input-output-copier"
|
||
>
|
||
Copy
|
||
</div>
|
||
</div>
|
||
<pre id="id00007163596982270759">
|
||
Yes
|
||
Yes
|
||
No
|
||
Yes
|
||
Yes
|
||
Yes
|
||
Yes
|
||
Yes
|
||
</pre
|
||
>
|
||
</div>
|
||
<div class="input">
|
||
<div class="title">
|
||
Input
|
||
<div
|
||
title="Copy"
|
||
data-clipboard-target="#id004021868626461702"
|
||
id="id006245115827740666"
|
||
class="input-output-copier"
|
||
>
|
||
Copy
|
||
</div>
|
||
</div>
|
||
<pre id="id004021868626461702">
|
||
6 9 6 6
|
||
1 2 4 9 18 19
|
||
2 17
|
||
1 18
|
||
5 4
|
||
2 11
|
||
5 17
|
||
6 8
|
||
4 3
|
||
3 3
|
||
6 6
|
||
</pre
|
||
>
|
||
</div>
|
||
<div class="output">
|
||
<div class="title">
|
||
Output
|
||
<div
|
||
title="Copy"
|
||
data-clipboard-target="#id0028814164650272367"
|
||
id="id003382640439163931"
|
||
class="input-output-copier"
|
||
>
|
||
Copy
|
||
</div>
|
||
</div>
|
||
<pre id="id0028814164650272367">
|
||
Yes
|
||
Yes
|
||
Yes
|
||
Yes
|
||
Yes
|
||
Yes
|
||
No
|
||
No
|
||
Yes
|
||
</pre
|
||
>
|
||
</div>
|
||
<div class="input">
|
||
<div class="title">
|
||
Input
|
||
<div
|
||
title="Copy"
|
||
data-clipboard-target="#id0036202103055617885"
|
||
id="id007376883974196634"
|
||
class="input-output-copier"
|
||
>
|
||
Copy
|
||
</div>
|
||
</div>
|
||
<pre id="id0036202103055617885">
|
||
4 1 1 10
|
||
1 8 10 19
|
||
2 1
|
||
</pre
|
||
>
|
||
</div>
|
||
<div class="output">
|
||
<div class="title">
|
||
Output
|
||
<div
|
||
title="Copy"
|
||
data-clipboard-target="#id008954713496747658"
|
||
id="id0012921296784619696"
|
||
class="input-output-copier"
|
||
>
|
||
Copy
|
||
</div>
|
||
</div>
|
||
<pre id="id008954713496747658">
|
||
Yes
|
||
</pre
|
||
>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<div class="note">
|
||
<div class="section-title">Note</div>
|
||
<p>Explanation of the first example:</p>
|
||
<p>
|
||
In the first testcase the destination rock is the same as
|
||
the starting rock, thus no jumps are required to reach it.
|
||
</p>
|
||
<p>
|
||
In the second testcase the frog can jump any distance in
|
||
the range
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1495"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1496"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>[</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1497">5</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1498"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>−</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1499">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1500"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>;</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1501">5</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1502"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>+</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1503">2</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1504"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>]</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-235">
|
||
[5 - 2; 5 + 2]
|
||
</script>
|
||
. Thus, it can reach rock number
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1505"
|
||
><span class="MJXp-mn" id="MJXp-Span-1506"
|
||
>5</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-236">
|
||
5
|
||
</script>
|
||
(by jumping
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1507"
|
||
><span class="MJXp-mn" id="MJXp-Span-1508"
|
||
>7</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-237">
|
||
7
|
||
</script>
|
||
to the right) and rock number
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1509"
|
||
><span class="MJXp-mn" id="MJXp-Span-1510"
|
||
>3</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-238">
|
||
3
|
||
</script>
|
||
(by jumping
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1511"
|
||
><span class="MJXp-mn" id="MJXp-Span-1512"
|
||
>3</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-239">
|
||
3
|
||
</script>
|
||
to the left). From rock number
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1513"
|
||
><span class="MJXp-mn" id="MJXp-Span-1514"
|
||
>3</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-240">
|
||
3
|
||
</script>
|
||
it can reach rock number
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1515"
|
||
><span class="MJXp-mn" id="MJXp-Span-1516"
|
||
>2</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-241">
|
||
2
|
||
</script>
|
||
(by jumping
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1517"
|
||
><span class="MJXp-mn" id="MJXp-Span-1518"
|
||
>5</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-242">
|
||
5
|
||
</script>
|
||
to the left). From rock number
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1519"
|
||
><span class="MJXp-mn" id="MJXp-Span-1520"
|
||
>2</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-243">
|
||
2
|
||
</script>
|
||
it can reach rock number
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1521"
|
||
><span class="MJXp-mn" id="MJXp-Span-1522"
|
||
>1</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-244">
|
||
1
|
||
</script>
|
||
(by jumping
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1523"
|
||
><span class="MJXp-mn" id="MJXp-Span-1524"
|
||
>4</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-245">
|
||
4
|
||
</script>
|
||
to the left). However, there is no way to reach rock
|
||
number
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1525"
|
||
><span class="MJXp-mn" id="MJXp-Span-1526"
|
||
>7</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-246">
|
||
7
|
||
</script>
|
||
.
|
||
</p>
|
||
<p>
|
||
In the third testcase the frog can jump any distance in
|
||
the range
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1527"
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1528"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>[</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1529">5</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1530"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>−</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1531">3</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1532"
|
||
style="margin-left: 0em; margin-right: 0.222em"
|
||
>;</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1533">5</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1534"
|
||
style="margin-left: 0.267em; margin-right: 0.267em"
|
||
>+</span
|
||
><span class="MJXp-mn" id="MJXp-Span-1535">3</span
|
||
><span
|
||
class="MJXp-mo"
|
||
id="MJXp-Span-1536"
|
||
style="margin-left: 0em; margin-right: 0em"
|
||
>]</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-247">
|
||
[5 - 3; 5 + 3]
|
||
</script>
|
||
. Thus, it can reach rock number
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1537"
|
||
><span class="MJXp-mn" id="MJXp-Span-1538"
|
||
>7</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-248">
|
||
7
|
||
</script>
|
||
by jumping to rock
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1539"
|
||
><span class="MJXp-mn" id="MJXp-Span-1540"
|
||
>5</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-249">
|
||
5
|
||
</script>
|
||
first and to
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1541"
|
||
><span class="MJXp-mn" id="MJXp-Span-1542"
|
||
>7</span
|
||
></span
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-250">
|
||
7
|
||
</script>
|
||
afterwards.
|
||
</p>
|
||
<p>
|
||
The fourth testcase is shown in the explanation for the
|
||
second testcase.
|
||
</p>
|
||
</div>
|
||
</div>
|
||
<p></p>
|
||
</div>
|
||
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|
||
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<div id="footer">
|
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<div>
|
||
<a href="https://codeforces.com/">Codeforces</a> (c) Copyright
|
||
2010-2025 Mike Mirzayanov
|
||
</div>
|
||
<div>The only programming contests Web 2.0 platform</div>
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||
</div>
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</div>
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|