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|
||
background-color: #aaa;
|
||
border: 1px solid;
|
||
border-radius: 3px;
|
||
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>
|
||
<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);
|
||
}
|
||
.MJXp-scale9 {
|
||
-webkit-transform: scaleX(0.9);
|
||
-moz-transform: scaleX(0.9);
|
||
-ms-transform: scaleX(0.9);
|
||
-o-transform: scaleX(0.9);
|
||
transform: scaleX(0.9);
|
||
}
|
||
.MathJax_PHTML .noError {
|
||
vertical-align:;
|
||
font-size: 90%;
|
||
text-align: left;
|
||
color: black;
|
||
padding: 1px 3px;
|
||
border: 1px solid;
|
||
}
|
||
</style>
|
||
<style type="text/css">
|
||
.MathJax_Display {
|
||
text-align: center;
|
||
margin: 1em 0em;
|
||
position: relative;
|
||
display: block !important;
|
||
text-indent: 0;
|
||
max-width: none;
|
||
max-height: none;
|
||
min-width: 0;
|
||
min-height: 0;
|
||
width: 100%;
|
||
}
|
||
.MathJax .merror {
|
||
background-color: #ffff88;
|
||
color: #cc0000;
|
||
border: 1px solid #cc0000;
|
||
padding: 1px 3px;
|
||
font-style: normal;
|
||
font-size: 90%;
|
||
}
|
||
.MathJax .MJX-monospace {
|
||
font-family: monospace;
|
||
}
|
||
.MathJax .MJX-sans-serif {
|
||
font-family: sans-serif;
|
||
}
|
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#MathJax_Tooltip {
|
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background-color: InfoBackground;
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||
color: InfoText;
|
||
border: 1px solid black;
|
||
box-shadow: 2px 2px 5px #aaaaaa;
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||
-webkit-box-shadow: 2px 2px 5px #aaaaaa;
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-moz-box-shadow: 2px 2px 5px #aaaaaa;
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-khtml-box-shadow: 2px 2px 5px #aaaaaa;
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filter: progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true');
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padding: 3px 4px;
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z-index: 401;
|
||
position: absolute;
|
||
left: 0;
|
||
top: 0;
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||
width: auto;
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||
height: auto;
|
||
display: none;
|
||
}
|
||
.MathJax {
|
||
display: inline;
|
||
font-style: normal;
|
||
font-weight: normal;
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||
line-height: normal;
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||
font-size: 100%;
|
||
font-size-adjust: none;
|
||
text-indent: 0;
|
||
text-align: left;
|
||
text-transform: none;
|
||
letter-spacing: normal;
|
||
word-spacing: normal;
|
||
word-wrap: normal;
|
||
white-space: nowrap;
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||
float: none;
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||
direction: ltr;
|
||
max-width: none;
|
||
max-height: none;
|
||
min-width: 0;
|
||
min-height: 0;
|
||
border: 0;
|
||
padding: 0;
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margin: 0;
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}
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.MathJax:focus,
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body :focus .MathJax {
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display: inline-table;
|
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}
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.MathJax.MathJax_FullWidth {
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||
text-align: center;
|
||
display: table-cell !important;
|
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width: 10000em !important;
|
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}
|
||
.MathJax img,
|
||
.MathJax nobr,
|
||
.MathJax a {
|
||
border: 0;
|
||
padding: 0;
|
||
margin: 0;
|
||
max-width: none;
|
||
max-height: none;
|
||
min-width: 0;
|
||
min-height: 0;
|
||
vertical-align: 0;
|
||
line-height: normal;
|
||
text-decoration: none;
|
||
}
|
||
img.MathJax_strut {
|
||
border: 0 !important;
|
||
padding: 0 !important;
|
||
margin: 0 !important;
|
||
vertical-align: 0 !important;
|
||
}
|
||
.MathJax span {
|
||
display: inline;
|
||
position: static;
|
||
border: 0;
|
||
padding: 0;
|
||
margin: 0;
|
||
vertical-align: 0;
|
||
line-height: normal;
|
||
text-decoration: none;
|
||
box-sizing: content-box;
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}
|
||
.MathJax nobr {
|
||
white-space: nowrap !important;
|
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}
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.MathJax img {
|
||
display: inline !important;
|
||
float: none !important;
|
||
}
|
||
.MathJax * {
|
||
transition: none;
|
||
-webkit-transition: none;
|
||
-moz-transition: none;
|
||
-ms-transition: none;
|
||
-o-transition: none;
|
||
}
|
||
.MathJax_Processing {
|
||
visibility: hidden;
|
||
position: fixed;
|
||
width: 0;
|
||
height: 0;
|
||
overflow: hidden;
|
||
}
|
||
.MathJax_Processed {
|
||
display: none !important;
|
||
}
|
||
.MathJax_test {
|
||
font-style: normal;
|
||
font-weight: normal;
|
||
font-size: 100%;
|
||
font-size-adjust: none;
|
||
text-indent: 0;
|
||
text-transform: none;
|
||
letter-spacing: normal;
|
||
word-spacing: normal;
|
||
overflow: hidden;
|
||
height: 1px;
|
||
}
|
||
.MathJax_test.mjx-test-display {
|
||
display: table !important;
|
||
}
|
||
.MathJax_test.mjx-test-inline {
|
||
display: inline !important;
|
||
margin-right: -1px;
|
||
}
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.MathJax_test.mjx-test-default {
|
||
display: block !important;
|
||
clear: both;
|
||
}
|
||
.MathJax_ex_box {
|
||
display: inline-block !important;
|
||
position: absolute;
|
||
overflow: hidden;
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min-height: 0;
|
||
max-height: none;
|
||
padding: 0;
|
||
border: 0;
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||
margin: 0;
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||
width: 1px;
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||
height: 60ex;
|
||
}
|
||
.MathJax_em_box {
|
||
display: inline-block !important;
|
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position: absolute;
|
||
overflow: hidden;
|
||
min-height: 0;
|
||
max-height: none;
|
||
padding: 0;
|
||
border: 0;
|
||
margin: 0;
|
||
width: 1px;
|
||
height: 60em;
|
||
}
|
||
.mjx-test-inline .MathJax_left_box {
|
||
display: inline-block;
|
||
width: 0;
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float: left;
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}
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|
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display: inline-block;
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width: 0;
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float: right;
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}
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.mjx-test-display .MathJax_right_box {
|
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display: table-cell !important;
|
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width: 10000em !important;
|
||
min-width: 0;
|
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max-width: none;
|
||
padding: 0;
|
||
border: 0;
|
||
margin: 0;
|
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}
|
||
.MathJax .MathJax_HitBox {
|
||
cursor: text;
|
||
background: white;
|
||
opacity: 0;
|
||
filter: alpha(opacity=0);
|
||
}
|
||
.MathJax .MathJax_HitBox * {
|
||
filter: none;
|
||
opacity: 1;
|
||
background: transparent;
|
||
}
|
||
#MathJax_Tooltip * {
|
||
filter: none;
|
||
opacity: 1;
|
||
background: transparent;
|
||
}
|
||
@font-face {
|
||
font-family: MathJax_Main;
|
||
src:
|
||
url('https://codeforces.com/mathjax.codeforces.org/fonts/HTML-CSS/TeX/woff/MathJax_Main-Regular.woff?V=2.7.9')
|
||
format('woff'),
|
||
url('https://codeforces.com/mathjax.codeforces.org/fonts/HTML-CSS/TeX/otf/MathJax_Main-Regular.otf?V=2.7.9')
|
||
format('opentype');
|
||
}
|
||
@font-face {
|
||
font-family: MathJax_Main;
|
||
src:
|
||
url('https://codeforces.com/mathjax.codeforces.org/fonts/HTML-CSS/TeX/woff/MathJax_Main-Bold.woff?V=2.7.9')
|
||
format('woff'),
|
||
url('https://codeforces.com/mathjax.codeforces.org/fonts/HTML-CSS/TeX/otf/MathJax_Main-Bold.otf?V=2.7.9')
|
||
format('opentype');
|
||
font-weight: bold;
|
||
}
|
||
@font-face {
|
||
font-family: MathJax_Main;
|
||
src:
|
||
url('https://codeforces.com/mathjax.codeforces.org/fonts/HTML-CSS/TeX/woff/MathJax_Main-Italic.woff?V=2.7.9')
|
||
format('woff'),
|
||
url('https://codeforces.com/mathjax.codeforces.org/fonts/HTML-CSS/TeX/otf/MathJax_Main-Italic.otf?V=2.7.9')
|
||
format('opentype');
|
||
font-style: italic;
|
||
}
|
||
@font-face {
|
||
font-family: MathJax_Math;
|
||
src:
|
||
url('https://codeforces.com/mathjax.codeforces.org/fonts/HTML-CSS/TeX/woff/MathJax_Math-Italic.woff?V=2.7.9')
|
||
format('woff'),
|
||
url('https://codeforces.com/mathjax.codeforces.org/fonts/HTML-CSS/TeX/otf/MathJax_Math-Italic.otf?V=2.7.9')
|
||
format('opentype');
|
||
font-style: italic;
|
||
}
|
||
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|
||
font-family: MathJax_Caligraphic;
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||
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||
url('https://codeforces.com/mathjax.codeforces.org/fonts/HTML-CSS/TeX/woff/MathJax_Caligraphic-Regular.woff?V=2.7.9')
|
||
format('woff'),
|
||
url('https://codeforces.com/mathjax.codeforces.org/fonts/HTML-CSS/TeX/otf/MathJax_Caligraphic-Regular.otf?V=2.7.9')
|
||
format('opentype');
|
||
}
|
||
@font-face {
|
||
font-family: MathJax_Size1;
|
||
src:
|
||
url('https://codeforces.com/mathjax.codeforces.org/fonts/HTML-CSS/TeX/woff/MathJax_Size1-Regular.woff?V=2.7.9')
|
||
format('woff'),
|
||
url('https://codeforces.com/mathjax.codeforces.org/fonts/HTML-CSS/TeX/otf/MathJax_Size1-Regular.otf?V=2.7.9')
|
||
format('opentype');
|
||
}
|
||
@font-face {
|
||
font-family: MathJax_Size2;
|
||
src:
|
||
url('https://codeforces.com/mathjax.codeforces.org/fonts/HTML-CSS/TeX/woff/MathJax_Size2-Regular.woff?V=2.7.9')
|
||
format('woff'),
|
||
url('https://codeforces.com/mathjax.codeforces.org/fonts/HTML-CSS/TeX/otf/MathJax_Size2-Regular.otf?V=2.7.9')
|
||
format('opentype');
|
||
}
|
||
@font-face {
|
||
font-family: MathJax_Size3;
|
||
src:
|
||
url('https://codeforces.com/mathjax.codeforces.org/fonts/HTML-CSS/TeX/woff/MathJax_Size3-Regular.woff?V=2.7.9')
|
||
format('woff'),
|
||
url('https://codeforces.com/mathjax.codeforces.org/fonts/HTML-CSS/TeX/otf/MathJax_Size3-Regular.otf?V=2.7.9')
|
||
format('opentype');
|
||
}
|
||
@font-face {
|
||
font-family: MathJax_Size4;
|
||
src:
|
||
url('https://codeforces.com/mathjax.codeforces.org/fonts/HTML-CSS/TeX/woff/MathJax_Size4-Regular.woff?V=2.7.9')
|
||
format('woff'),
|
||
url('https://codeforces.com/mathjax.codeforces.org/fonts/HTML-CSS/TeX/otf/MathJax_Size4-Regular.otf?V=2.7.9')
|
||
format('opentype');
|
||
}
|
||
.MathJax .noError {
|
||
vertical-align:;
|
||
font-size: 90%;
|
||
text-align: left;
|
||
color: black;
|
||
padding: 1px 3px;
|
||
border: 1px solid;
|
||
}
|
||
</style>
|
||
</head>
|
||
<body class=" ">
|
||
<div
|
||
style="
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|
||
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|
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top: 0px;
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||
height: 1px;
|
||
width: auto;
|
||
padding: 0px;
|
||
border: 0px;
|
||
margin: 0px;
|
||
text-align: left;
|
||
text-indent: 0px;
|
||
text-transform: none;
|
||
line-height: normal;
|
||
letter-spacing: normal;
|
||
word-spacing: normal;
|
||
"
|
||
>
|
||
<div id="MathJax_Hidden"></div>
|
||
</div>
|
||
<div id="MathJax_Message" style="display: none"></div>
|
||
<span
|
||
style="display: none"
|
||
class="csrf-token"
|
||
data-csrf="df9f60cd2f719a4222b54721ae7989a3"
|
||
> </span
|
||
>
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||
<div class="notificationTextCleaner" style="font-size: 0"></div>
|
||
<div
|
||
class="button-up"
|
||
style="
|
||
display: none;
|
||
opacity: 0.7;
|
||
width: 30px;
|
||
height: 100%;
|
||
position: fixed;
|
||
left: 0px;
|
||
top: 0px;
|
||
cursor: pointer;
|
||
text-align: center;
|
||
line-height: 30px;
|
||
color: rgb(211, 219, 228);
|
||
font-weight: bold;
|
||
font-size: 20px;
|
||
"
|
||
>
|
||
<i class="icon-circle-arrow-up"></i>
|
||
</div>
|
||
<div class="verdictPrototypeDiv" style="display: none"></div>
|
||
<script type="text/javascript">
|
||
String.prototype.hashCode = function () {
|
||
var hash = 0,
|
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i,
|
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chr
|
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if (this.length === 0) return hash
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for (i = 0; i < this.length; i++) {
|
||
chr = this.charCodeAt(i)
|
||
hash = (hash << 5) - hash + chr
|
||
hash |= 0 // Convert to 32bit integer
|
||
}
|
||
return hash
|
||
}
|
||
|
||
var queryMobile = Codeforces.queryString.mobile
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if (queryMobile === 'true' || queryMobile === 'false') {
|
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Codeforces.putToStorage('useMobile', queryMobile === 'true')
|
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} else {
|
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var useMobile = Codeforces.getFromStorage('useMobile')
|
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if (useMobile === true || useMobile === false) {
|
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if (useMobile != false) {
|
||
Codeforces.redirect(
|
||
Codeforces.updateUrlParameter(
|
||
document.location.href,
|
||
'mobile',
|
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useMobile
|
||
)
|
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)
|
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}
|
||
}
|
||
}
|
||
</script>
|
||
<script type="text/javascript">
|
||
if (window.parent.frames.length > 0) {
|
||
window.stop()
|
||
}
|
||
</script>
|
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<script type="text/javascript">
|
||
$(document).ready(function () {
|
||
;(function () {
|
||
jQuery.expr[':'].containsCI = function (elem, index, match) {
|
||
return (
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||
!match ||
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||
!match.length ||
|
||
match.length < 4 ||
|
||
!match[3] ||
|
||
(elem.textContent || elem.innerText || jQuery(elem).text() || '')
|
||
.toLowerCase()
|
||
.indexOf(match[3].toLowerCase()) >= 0
|
||
)
|
||
}
|
||
})(jQuery)
|
||
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$.ajaxPrefilter(function (options, originalOptions, xhr) {
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var csrf = Codeforces.getCsrfToken()
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var data = originalOptions.data
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if (originalOptions.data !== undefined) {
|
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if (
|
||
Object.prototype.toString.call(originalOptions.data) ===
|
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'[object String]'
|
||
) {
|
||
data = $.deparam(originalOptions.data)
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}
|
||
} else {
|
||
data = {}
|
||
}
|
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options.data = $.param($.extend(data, { csrf_token: csrf }))
|
||
}
|
||
})
|
||
|
||
window.getCodeforcesServerTime = function (callback) {
|
||
$.post('/data/time', {}, callback, 'json')
|
||
}
|
||
|
||
window.updateTypography = function () {
|
||
$('div.ttypography code').addClass('tt')
|
||
$('div.ttypography pre>code')
|
||
.addClass('prettyprint')
|
||
.removeClass('tt')
|
||
$('div.ttypography table').addClass('bordertable')
|
||
prettyPrint()
|
||
}
|
||
|
||
$.ajaxSetup({
|
||
scriptCharset: 'utf-8',
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contentType: 'application/x-www-form-urlencoded; charset=UTF-8',
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'X-Csrf-Token': Codeforces.getCsrfToken()
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const url = new URL(settings.url, window.location.href)
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const urlHref = url.href
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url.searchParams.set('rv', Math.random().toString(36).substr(2, 9)) // Generate a random value
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settings.url = url.href
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window.updateTypography()
|
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Codeforces.signForms()
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Codeforces.applyDatatableJs(
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'Hold Ctrl+Alt and click to hide column. Also, you can drag&drop columns to reorder them.'
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)
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setTimeout(function () {
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$('.second-level-menu-list').lavaLamp({
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fx: 'backout',
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Codeforces.countdown()
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$("a[rel='photobox']").colorbox()
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|
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function showEventCatcherUserMessage(json) {
|
||
if (json.t === 's') {
|
||
var points = json.d[5]
|
||
var passedTestCount = json.d[7]
|
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var judgedTestCount = json.d[8]
|
||
var verdict = preparedVerdictFormats[json.d[12]]
|
||
var verdictPrototypeDiv = $('.verdictPrototypeDiv')
|
||
verdictPrototypeDiv.html(verdict)
|
||
if (judgedTestCount != null && judgedTestCount != undefined) {
|
||
verdictPrototypeDiv
|
||
.find('.verdict-format-judged')
|
||
.text(judgedTestCount)
|
||
}
|
||
if (passedTestCount != null && passedTestCount != undefined) {
|
||
verdictPrototypeDiv
|
||
.find('.verdict-format-passed')
|
||
.text(passedTestCount)
|
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if (points != null && points != undefined) {
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verdictPrototypeDiv.find('.verdict-format-points').text(points)
|
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Codeforces.showMessage(verdictPrototypeDiv.text())
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$('.clickable-title').each(function () {
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Virtual contest is a way to take part in past contest, as close
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as possible to participation on time. It is supported only ICPC
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virtual contest is not for you - solve these problems in the
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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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<li>
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<a
|
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href="/blog/entry/92864"
|
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title="Educational Codeforces Round 111 Editorial"
|
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target="_blank"
|
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>Tutorial</a
|
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>
|
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|
||
resourceids="14021:14022"
|
||
resourcename="Tutorial"
|
||
resourcemanual="true"
|
||
src="//codeforces.org/s/76290/images/icons/close-10x10.png"
|
||
style="
|
||
position: relative;
|
||
bottom: -1px;
|
||
left: 1px;
|
||
cursor: pointer;
|
||
"
|
||
/></span>
|
||
<div style="clear: both"></div>
|
||
</li>
|
||
</ul>
|
||
</div>
|
||
</div>
|
||
<div id="pageContent" class="content-with-sidebar">
|
||
<div class="second-level-menu">
|
||
<ul class="second-level-menu-list">
|
||
<li
|
||
class="backLava"
|
||
style="
|
||
position: absolute;
|
||
display: block;
|
||
margin: 0px;
|
||
padding: 0px;
|
||
left: 0px;
|
||
top: 0px;
|
||
width: 79px;
|
||
height: 20px;
|
||
"
|
||
>
|
||
<div class="leftLava"></div>
|
||
<div class="bottomLava"></div>
|
||
<div class="cornerLava"></div>
|
||
</li>
|
||
<li class="current selectedLava">
|
||
<a href="/contest/1550">Problems</a>
|
||
</li>
|
||
<li><a href="/contest/1550/submit">Submit Code</a></li>
|
||
<li><a href="/contest/1550/my">My Submissions</a></li>
|
||
<li><a href="/contest/1550/status">Status</a></li>
|
||
<li><a href="/contest/1550/hacks">Hacks</a></li>
|
||
<li><a href="/contest/1550/standings">Standings</a></li>
|
||
<li><a href="/contest/1550/customtest">Custom Invocation</a></li>
|
||
</ul>
|
||
</div>
|
||
|
||
<style>
|
||
#facebox .content:has(.diff-popup) {
|
||
width: 90vw;
|
||
max-width: 120rem !important;
|
||
}
|
||
|
||
.testCaseMarker {
|
||
position: absolute;
|
||
font-weight: bold;
|
||
font-size: 1rem;
|
||
}
|
||
|
||
.diff-popup {
|
||
width: 90vw;
|
||
max-width: 120rem !important;
|
||
display: none;
|
||
overflow: auto;
|
||
}
|
||
|
||
.input-output-copier {
|
||
font-size: 1.2rem;
|
||
float: right;
|
||
color: #888 !important;
|
||
cursor: pointer;
|
||
border: 1px solid rgb(185, 185, 185);
|
||
padding: 3px;
|
||
margin: 1px;
|
||
line-height: 1.1rem;
|
||
text-transform: none;
|
||
}
|
||
|
||
.input-output-copier:hover {
|
||
background-color: #def;
|
||
}
|
||
|
||
.test-explanation textarea {
|
||
width: 100%;
|
||
height: 1.5em;
|
||
}
|
||
|
||
.pending-submission-message {
|
||
color: darkorange !important;
|
||
}
|
||
</style>
|
||
<script>
|
||
const OPENING_SPACE = String.fromCharCode(1001)
|
||
const CLOSING_SPACE = String.fromCharCode(1002)
|
||
|
||
const nodeToText = function (node, pre) {
|
||
let result = []
|
||
|
||
if (
|
||
node.tagName === 'SCRIPT' ||
|
||
node.tagName === 'math' ||
|
||
(node.classList &&
|
||
node.classList.contains('input-output-copier'))
|
||
)
|
||
return []
|
||
|
||
if (node.tagName === 'NOBR') {
|
||
result.push(OPENING_SPACE)
|
||
}
|
||
|
||
if (node.nodeType === Node.TEXT_NODE) {
|
||
let s = node.textContent
|
||
if (!pre) {
|
||
s = s.replace(/\s+/g, ' ')
|
||
}
|
||
if (s.length > 0) {
|
||
result.push(s)
|
||
}
|
||
}
|
||
|
||
if (pre && node.tagName === 'BR') {
|
||
result.push('\n')
|
||
}
|
||
|
||
node.childNodes.forEach(function (child) {
|
||
result.push(nodeToText(child, node.tagName === 'PRE').join(''))
|
||
})
|
||
|
||
if (
|
||
node.tagName === 'DIV' ||
|
||
node.tagName === 'P' ||
|
||
node.tagName === 'PRE' ||
|
||
node.tagName === 'UL' ||
|
||
node.tagName === 'LI'
|
||
) {
|
||
result.push('\n')
|
||
}
|
||
|
||
if (node.tagName === 'NOBR') {
|
||
result.push(CLOSING_SPACE)
|
||
}
|
||
|
||
return result
|
||
}
|
||
|
||
const isSpecial = function (c) {
|
||
return (
|
||
c === ',' || c === '.' || c === ';' || c === ')' || c === ' '
|
||
)
|
||
}
|
||
|
||
const convertStatementToText = function (statmentNode) {
|
||
const text = nodeToText(statmentNode, false)
|
||
.join('')
|
||
.replace(/ +/g, ' ')
|
||
.replace(/\n\n+/g, '\n\n')
|
||
let result = []
|
||
for (let i = 0; i < text.length; i++) {
|
||
const c = text.charAt(i)
|
||
if (c === OPENING_SPACE) {
|
||
if (
|
||
!(
|
||
(i > 0 && text.charAt(i - 1) === '(') ||
|
||
(result.length > 0 && result[result.length - 1] === ' ')
|
||
)
|
||
) {
|
||
result.push('+')
|
||
}
|
||
} else if (c === CLOSING_SPACE) {
|
||
if (!(i + 1 < text.length && isSpecial(text.charAt(i + 1)))) {
|
||
result.push('-')
|
||
}
|
||
} else {
|
||
result.push(c)
|
||
}
|
||
}
|
||
return result
|
||
.join('')
|
||
.split('\n')
|
||
.map((value) => value.trim())
|
||
.join('\n')
|
||
}
|
||
</script>
|
||
<div class="diff-popup"></div>
|
||
|
||
<div
|
||
class="problemindexholder"
|
||
problemindex="A"
|
||
data-uuid="ps_cdca4b584b10da43dcb13b587596b603b8370a1a"
|
||
>
|
||
<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">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
|
||
</div>
|
||
<div class="output-file output-standard">
|
||
<div class="property-title">output</div>
|
||
standard output
|
||
</div>
|
||
</div>
|
||
<div>
|
||
<p>
|
||
Let's call an array
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-1"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-2"
|
||
>a</span
|
||
></span
|
||
></span
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-1-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-1"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-2"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-3"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>a</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-1">
|
||
a
|
||
</script>
|
||
consisting of
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-3"
|
||
><span class="MJXp-mi MJXp-italic" id="MJXp-Span-4"
|
||
>n</span
|
||
></span
|
||
></span
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-2-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-4"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-5"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-6"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>n</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></span
|
||
>
|
||
<script type="math/tex" id="MathJax-Element-2">
|
||
n
|
||
</script>
|
||
positive (greater than
|
||
<span class="MathJax_Preview" style="color: inherit"
|
||
><span class="MJXp-math" id="MJXp-Span-5"
|
||
><span class="MJXp-mn" id="MJXp-Span-6">0</span></span
|
||
></span
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-3-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-7"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-8"
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-9"
|
||
style="font-family: MathJax_Main"
|
||
>0</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-4-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-10"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-11"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-12"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>i</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-5-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-13"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-14"
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-15"
|
||
style="font-family: MathJax_Main"
|
||
>1</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-6-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-16"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-17"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-18"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>n</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-7-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-19"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-20"
|
||
><span class="msubsup" id="MathJax-Span-21"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0.848em;
|
||
height: 0px;
|
||
"
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
clip: rect(
|
||
3.365em,
|
||
1000.51em,
|
||
4.167em,
|
||
-1000em
|
||
);
|
||
top: -3.981em;
|
||
left: 0em;
|
||
"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-22"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>a</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
top: -3.831em;
|
||
left: 0.529em;
|
||
"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-23"
|
||
style="
|
||
font-size: 70.7%;
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>i</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span></span></span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-24"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>=</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-25"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>1</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-8-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-26"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-27"
|
||
><span class="msubsup" id="MathJax-Span-28"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0.848em;
|
||
height: 0px;
|
||
"
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
clip: rect(
|
||
3.365em,
|
||
1000.51em,
|
||
4.167em,
|
||
-1000em
|
||
);
|
||
top: -3.981em;
|
||
left: 0em;
|
||
"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-29"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>a</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
top: -3.831em;
|
||
left: 0.529em;
|
||
"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-30"
|
||
style="
|
||
font-size: 70.7%;
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>i</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span></span></span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-31"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.222em;
|
||
"
|
||
>−</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-32"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.222em;
|
||
"
|
||
>1</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-9-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-33"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-34"
|
||
><span class="msubsup" id="MathJax-Span-35"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0.848em;
|
||
height: 0px;
|
||
"
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
clip: rect(
|
||
3.365em,
|
||
1000.51em,
|
||
4.167em,
|
||
-1000em
|
||
);
|
||
top: -3.981em;
|
||
left: 0em;
|
||
"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-36"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>a</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
top: -3.831em;
|
||
left: 0.529em;
|
||
"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-37"
|
||
style="
|
||
font-size: 70.7%;
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>i</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span></span></span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-38"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.222em;
|
||
"
|
||
>−</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-39"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.222em;
|
||
"
|
||
>2</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-10-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-40"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-41"
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-42"
|
||
style="font-family: MathJax_Main"
|
||
>[</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-43"
|
||
style="font-family: MathJax_Main"
|
||
>5</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-44"
|
||
style="font-family: MathJax_Main"
|
||
>,</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-45"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.167em;
|
||
"
|
||
>3</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-46"
|
||
style="font-family: MathJax_Main"
|
||
>,</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-47"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.167em;
|
||
"
|
||
>1</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-48"
|
||
style="font-family: MathJax_Main"
|
||
>]</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-11-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-49"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-50"
|
||
><span class="msubsup" id="MathJax-Span-51"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0.958em;
|
||
height: 0px;
|
||
"
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
clip: rect(
|
||
3.365em,
|
||
1000.51em,
|
||
4.167em,
|
||
-1000em
|
||
);
|
||
top: -3.981em;
|
||
left: 0em;
|
||
"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-52"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>a</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
top: -3.831em;
|
||
left: 0.529em;
|
||
"
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-53"
|
||
style="
|
||
font-size: 70.7%;
|
||
font-family: MathJax_Main;
|
||
"
|
||
>1</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span></span></span></span></span></span></span></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-12-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-54"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-55"
|
||
><span class="msubsup" id="MathJax-Span-56"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0.958em;
|
||
height: 0px;
|
||
"
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
clip: rect(
|
||
3.365em,
|
||
1000.51em,
|
||
4.167em,
|
||
-1000em
|
||
);
|
||
top: -3.981em;
|
||
left: 0em;
|
||
"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-57"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>a</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
top: -3.831em;
|
||
left: 0.529em;
|
||
"
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-58"
|
||
style="
|
||
font-size: 70.7%;
|
||
font-family: MathJax_Main;
|
||
"
|
||
>1</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span></span></span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-59"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.222em;
|
||
"
|
||
>−</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-60"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.222em;
|
||
"
|
||
>2</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-61"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>=</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-62"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>3</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-13-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-63"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-64"
|
||
><span class="msubsup" id="MathJax-Span-65"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0.958em;
|
||
height: 0px;
|
||
"
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
clip: rect(
|
||
3.365em,
|
||
1000.51em,
|
||
4.167em,
|
||
-1000em
|
||
);
|
||
top: -3.981em;
|
||
left: 0em;
|
||
"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-66"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>a</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
top: -3.831em;
|
||
left: 0.529em;
|
||
"
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-67"
|
||
style="
|
||
font-size: 70.7%;
|
||
font-family: MathJax_Main;
|
||
"
|
||
>2</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span></span></span></span></span></span></span></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-14-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-68"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-69"
|
||
><span class="msubsup" id="MathJax-Span-70"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0.958em;
|
||
height: 0px;
|
||
"
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
clip: rect(
|
||
3.365em,
|
||
1000.51em,
|
||
4.167em,
|
||
-1000em
|
||
);
|
||
top: -3.981em;
|
||
left: 0em;
|
||
"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-71"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>a</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
top: -3.831em;
|
||
left: 0.529em;
|
||
"
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-72"
|
||
style="
|
||
font-size: 70.7%;
|
||
font-family: MathJax_Main;
|
||
"
|
||
>2</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span></span></span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-73"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.222em;
|
||
"
|
||
>−</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-74"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.222em;
|
||
"
|
||
>2</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-75"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>=</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-76"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>1</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-15-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-77"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-78"
|
||
><span class="msubsup" id="MathJax-Span-79"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0.958em;
|
||
height: 0px;
|
||
"
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
clip: rect(
|
||
3.365em,
|
||
1000.51em,
|
||
4.167em,
|
||
-1000em
|
||
);
|
||
top: -3.981em;
|
||
left: 0em;
|
||
"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-80"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>a</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
top: -3.831em;
|
||
left: 0.529em;
|
||
"
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-81"
|
||
style="
|
||
font-size: 70.7%;
|
||
font-family: MathJax_Main;
|
||
"
|
||
>3</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span></span></span></span></span></span></span></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-16-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-82"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-83"
|
||
><span class="msubsup" id="MathJax-Span-84"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0.958em;
|
||
height: 0px;
|
||
"
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
clip: rect(
|
||
3.365em,
|
||
1000.51em,
|
||
4.167em,
|
||
-1000em
|
||
);
|
||
top: -3.981em;
|
||
left: 0em;
|
||
"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-85"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>a</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
top: -3.831em;
|
||
left: 0.529em;
|
||
"
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-86"
|
||
style="
|
||
font-size: 70.7%;
|
||
font-family: MathJax_Main;
|
||
"
|
||
>3</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span></span></span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-87"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>=</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-88"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>1</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-17-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-89"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-90"
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-91"
|
||
style="font-family: MathJax_Main"
|
||
>[</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-92"
|
||
style="font-family: MathJax_Main"
|
||
>1</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-93"
|
||
style="font-family: MathJax_Main"
|
||
>,</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-94"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.167em;
|
||
"
|
||
>2</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-95"
|
||
style="font-family: MathJax_Main"
|
||
>,</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-96"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.167em;
|
||
"
|
||
>2</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-97"
|
||
style="font-family: MathJax_Main"
|
||
>,</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-98"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.167em;
|
||
"
|
||
>2</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-99"
|
||
style="font-family: MathJax_Main"
|
||
>,</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-100"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.167em;
|
||
"
|
||
>2</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-101"
|
||
style="font-family: MathJax_Main"
|
||
>]</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-18-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-102"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-103"
|
||
><span class="msubsup" id="MathJax-Span-104"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0.958em;
|
||
height: 0px;
|
||
"
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
clip: rect(
|
||
3.365em,
|
||
1000.51em,
|
||
4.167em,
|
||
-1000em
|
||
);
|
||
top: -3.981em;
|
||
left: 0em;
|
||
"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-105"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>a</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
top: -3.831em;
|
||
left: 0.529em;
|
||
"
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-106"
|
||
style="
|
||
font-size: 70.7%;
|
||
font-family: MathJax_Main;
|
||
"
|
||
>1</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span></span></span></span></span></span></span></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-19-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-107"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-108"
|
||
><span class="msubsup" id="MathJax-Span-109"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0.958em;
|
||
height: 0px;
|
||
"
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
clip: rect(
|
||
3.365em,
|
||
1000.51em,
|
||
4.167em,
|
||
-1000em
|
||
);
|
||
top: -3.981em;
|
||
left: 0em;
|
||
"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-110"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>a</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
top: -3.831em;
|
||
left: 0.529em;
|
||
"
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-111"
|
||
style="
|
||
font-size: 70.7%;
|
||
font-family: MathJax_Main;
|
||
"
|
||
>1</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span></span></span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-112"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>=</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-113"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>1</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-20-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-114"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-115"
|
||
><span class="msubsup" id="MathJax-Span-116"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0.848em;
|
||
height: 0px;
|
||
"
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
clip: rect(
|
||
3.365em,
|
||
1000.51em,
|
||
4.167em,
|
||
-1000em
|
||
);
|
||
top: -3.981em;
|
||
left: 0em;
|
||
"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-117"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>a</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
top: -3.831em;
|
||
left: 0.529em;
|
||
"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-118"
|
||
style="
|
||
font-size: 70.7%;
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>i</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span></span></span></span></span></span></span></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-21-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-119"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-120"
|
||
><span class="msubsup" id="MathJax-Span-121"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0.848em;
|
||
height: 0px;
|
||
"
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
clip: rect(
|
||
3.365em,
|
||
1000.51em,
|
||
4.167em,
|
||
-1000em
|
||
);
|
||
top: -3.981em;
|
||
left: 0em;
|
||
"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-122"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>a</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
top: -3.831em;
|
||
left: 0.529em;
|
||
"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-123"
|
||
style="
|
||
font-size: 70.7%;
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>i</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span></span></span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-124"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.222em;
|
||
"
|
||
>−</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-125"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.222em;
|
||
"
|
||
>1</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-126"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>=</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-127"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>1</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-22-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-128"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-129"
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-130"
|
||
style="font-family: MathJax_Main"
|
||
>[</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-131"
|
||
style="font-family: MathJax_Main"
|
||
>1</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-132"
|
||
style="font-family: MathJax_Main"
|
||
>,</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-133"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.167em;
|
||
"
|
||
>4</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-134"
|
||
style="font-family: MathJax_Main"
|
||
>]</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-23-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-135"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-136"
|
||
><span class="msubsup" id="MathJax-Span-137"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0.958em;
|
||
height: 0px;
|
||
"
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
clip: rect(
|
||
3.365em,
|
||
1000.51em,
|
||
4.167em,
|
||
-1000em
|
||
);
|
||
top: -3.981em;
|
||
left: 0em;
|
||
"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-138"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>a</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
top: -3.831em;
|
||
left: 0.529em;
|
||
"
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-139"
|
||
style="
|
||
font-size: 70.7%;
|
||
font-family: MathJax_Main;
|
||
"
|
||
>2</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span></span></span></span></span></span></span></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-24-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-140"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-141"
|
||
><span class="msubsup" id="MathJax-Span-142"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0.958em;
|
||
height: 0px;
|
||
"
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
clip: rect(
|
||
3.365em,
|
||
1000.51em,
|
||
4.167em,
|
||
-1000em
|
||
);
|
||
top: -3.981em;
|
||
left: 0em;
|
||
"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-143"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>a</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
top: -3.831em;
|
||
left: 0.529em;
|
||
"
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-144"
|
||
style="
|
||
font-size: 70.7%;
|
||
font-family: MathJax_Main;
|
||
"
|
||
>2</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span></span></span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-145"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.222em;
|
||
"
|
||
>−</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-146"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.222em;
|
||
"
|
||
>2</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-147"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>=</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-148"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>2</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-25-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-149"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-150"
|
||
><span class="msubsup" id="MathJax-Span-151"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0.958em;
|
||
height: 0px;
|
||
"
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
clip: rect(
|
||
3.365em,
|
||
1000.51em,
|
||
4.167em,
|
||
-1000em
|
||
);
|
||
top: -3.981em;
|
||
left: 0em;
|
||
"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-152"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>a</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
top: -3.831em;
|
||
left: 0.529em;
|
||
"
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-153"
|
||
style="
|
||
font-size: 70.7%;
|
||
font-family: MathJax_Main;
|
||
"
|
||
>2</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span></span></span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-154"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.222em;
|
||
"
|
||
>−</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-155"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.222em;
|
||
"
|
||
>1</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-156"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>=</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-157"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>3</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-26-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-158"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-159"
|
||
><span class="msubsup" id="MathJax-Span-160"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0.958em;
|
||
height: 0px;
|
||
"
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
clip: rect(
|
||
3.365em,
|
||
1000.51em,
|
||
4.167em,
|
||
-1000em
|
||
);
|
||
top: -3.981em;
|
||
left: 0em;
|
||
"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-161"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>a</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
top: -3.831em;
|
||
left: 0.529em;
|
||
"
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-162"
|
||
style="
|
||
font-size: 70.7%;
|
||
font-family: MathJax_Main;
|
||
"
|
||
>2</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span></span></span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-163"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>≠</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-164"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>1</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-27-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-165"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-166"
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-167"
|
||
style="font-family: MathJax_Main"
|
||
>[</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-168"
|
||
style="font-family: MathJax_Main"
|
||
>2</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-169"
|
||
style="font-family: MathJax_Main"
|
||
>]</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-28-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-170"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-171"
|
||
><span class="msubsup" id="MathJax-Span-172"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0.958em;
|
||
height: 0px;
|
||
"
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
clip: rect(
|
||
3.365em,
|
||
1000.51em,
|
||
4.167em,
|
||
-1000em
|
||
);
|
||
top: -3.981em;
|
||
left: 0em;
|
||
"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-173"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>a</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
top: -3.831em;
|
||
left: 0.529em;
|
||
"
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-174"
|
||
style="
|
||
font-size: 70.7%;
|
||
font-family: MathJax_Main;
|
||
"
|
||
>1</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span></span></span></span></span></span></span></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-29-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-175"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-176"
|
||
><span class="msubsup" id="MathJax-Span-177"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0.958em;
|
||
height: 0px;
|
||
"
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
clip: rect(
|
||
3.365em,
|
||
1000.51em,
|
||
4.167em,
|
||
-1000em
|
||
);
|
||
top: -3.981em;
|
||
left: 0em;
|
||
"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-178"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>a</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
top: -3.831em;
|
||
left: 0.529em;
|
||
"
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-179"
|
||
style="
|
||
font-size: 70.7%;
|
||
font-family: MathJax_Main;
|
||
"
|
||
>1</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span></span></span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-180"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.222em;
|
||
"
|
||
>−</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-181"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.222em;
|
||
"
|
||
>1</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-182"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>=</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-183"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>1</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-30-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-184"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-185"
|
||
><span class="msubsup" id="MathJax-Span-186"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0.958em;
|
||
height: 0px;
|
||
"
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
clip: rect(
|
||
3.365em,
|
||
1000.51em,
|
||
4.167em,
|
||
-1000em
|
||
);
|
||
top: -3.981em;
|
||
left: 0em;
|
||
"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-187"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>a</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
top: -3.831em;
|
||
left: 0.529em;
|
||
"
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-188"
|
||
style="
|
||
font-size: 70.7%;
|
||
font-family: MathJax_Main;
|
||
"
|
||
>1</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span></span></span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-189"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.222em;
|
||
"
|
||
>−</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-190"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.222em;
|
||
"
|
||
>2</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-191"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>=</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-192"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>0</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-31-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-193"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-194"
|
||
><span class="msubsup" id="MathJax-Span-195"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0.958em;
|
||
height: 0px;
|
||
"
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
clip: rect(
|
||
3.365em,
|
||
1000.51em,
|
||
4.167em,
|
||
-1000em
|
||
);
|
||
top: -3.981em;
|
||
left: 0em;
|
||
"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-196"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>a</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
top: -3.831em;
|
||
left: 0.529em;
|
||
"
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-197"
|
||
style="
|
||
font-size: 70.7%;
|
||
font-family: MathJax_Main;
|
||
"
|
||
>1</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span></span></span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-198"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>≠</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-199"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>1</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-32-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-200"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-201"
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-202"
|
||
style="font-family: MathJax_Main"
|
||
>[</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-203"
|
||
style="font-family: MathJax_Main"
|
||
>2</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-204"
|
||
style="font-family: MathJax_Main"
|
||
>,</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-205"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.167em;
|
||
"
|
||
>1</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-206"
|
||
style="font-family: MathJax_Main"
|
||
>,</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-207"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.167em;
|
||
"
|
||
>3</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-208"
|
||
style="font-family: MathJax_Main"
|
||
>]</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
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|
||
></span
|
||
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|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-33-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-209"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-210"
|
||
><span class="msubsup" id="MathJax-Span-211"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0.958em;
|
||
height: 0px;
|
||
"
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
clip: rect(
|
||
3.365em,
|
||
1000.51em,
|
||
4.167em,
|
||
-1000em
|
||
);
|
||
top: -3.981em;
|
||
left: 0em;
|
||
"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-212"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>a</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
top: -3.831em;
|
||
left: 0.529em;
|
||
"
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-213"
|
||
style="
|
||
font-size: 70.7%;
|
||
font-family: MathJax_Main;
|
||
"
|
||
>1</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span></span></span></span></span></span></span></nobr
|
||
></span>
|
||
<script type="math/tex" id="MathJax-Element-33">
|
||
a_1
|
||
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|
||
, the number
|
||
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|
||
><span class="MJXp-math" id="MJXp-Span-181"
|
||
><span class="MJXp-msubsup" id="MJXp-Span-182"
|
||
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|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-183"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
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|
||
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
|
||
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|
||
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|
||
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
|
||
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|
||
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|
||
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|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-34-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-214"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-215"
|
||
><span class="msubsup" id="MathJax-Span-216"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0.958em;
|
||
height: 0px;
|
||
"
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
clip: rect(
|
||
3.365em,
|
||
1000.51em,
|
||
4.167em,
|
||
-1000em
|
||
);
|
||
top: -3.981em;
|
||
left: 0em;
|
||
"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-217"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>a</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
top: -3.831em;
|
||
left: 0.529em;
|
||
"
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-218"
|
||
style="
|
||
font-size: 70.7%;
|
||
font-family: MathJax_Main;
|
||
"
|
||
>1</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span></span></span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-219"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.222em;
|
||
"
|
||
>−</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-220"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.222em;
|
||
"
|
||
>1</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-221"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>=</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-222"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>1</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
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|
||
>
|
||
<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"
|
||
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|
||
><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
|
||
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|
||
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|
||
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|
||
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|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-35-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
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|
||
><span class="math" id="MathJax-Span-223"
|
||
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|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-224"
|
||
><span class="msubsup" id="MathJax-Span-225"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0.958em;
|
||
height: 0px;
|
||
"
|
||
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|
||
style="
|
||
position: absolute;
|
||
clip: rect(
|
||
3.365em,
|
||
1000.51em,
|
||
4.167em,
|
||
-1000em
|
||
);
|
||
top: -3.981em;
|
||
left: 0em;
|
||
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|
||
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|
||
class="mi"
|
||
id="MathJax-Span-226"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>a</span
|
||
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|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
top: -3.831em;
|
||
left: 0.529em;
|
||
"
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-227"
|
||
style="
|
||
font-size: 70.7%;
|
||
font-family: MathJax_Main;
|
||
"
|
||
>2</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span></span></span></span></span></span></span></nobr
|
||
></span>
|
||
<script type="math/tex" id="MathJax-Element-35">
|
||
a_2
|
||
</script>
|
||
, the condition
|
||
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|
||
><span class="MJXp-math" id="MJXp-Span-193"
|
||
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|
||
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|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-195"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
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|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-196"
|
||
style="vertical-align: -0.4em"
|
||
>2</span
|
||
></span
|
||
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|
||
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
|
||
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|
||
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|
||
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|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-36-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
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|
||
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|
||
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|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-229"
|
||
><span class="msubsup" id="MathJax-Span-230"
|
||
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|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0.958em;
|
||
height: 0px;
|
||
"
|
||
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|
||
style="
|
||
position: absolute;
|
||
clip: rect(
|
||
3.365em,
|
||
1000.51em,
|
||
4.167em,
|
||
-1000em
|
||
);
|
||
top: -3.981em;
|
||
left: 0em;
|
||
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|
||
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|
||
class="mi"
|
||
id="MathJax-Span-231"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>a</span
|
||
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|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
top: -3.831em;
|
||
left: 0.529em;
|
||
"
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-232"
|
||
style="
|
||
font-size: 70.7%;
|
||
font-family: MathJax_Main;
|
||
"
|
||
>2</span
|
||
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|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span></span></span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-233"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>=</span
|
||
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|
||
class="mn"
|
||
id="MathJax-Span-234"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>1</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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|
||
>
|
||
<script type="math/tex" id="MathJax-Element-36">
|
||
a_2 = 1
|
||
</script>
|
||
holds; for
|
||
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|
||
><span class="MJXp-math" id="MJXp-Span-199"
|
||
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|
||
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|
||
class="MJXp-mi MJXp-italic"
|
||
id="MJXp-Span-201"
|
||
style="margin-right: 0.05em"
|
||
>a</span
|
||
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|
||
class="MJXp-mn MJXp-script"
|
||
id="MJXp-Span-202"
|
||
style="vertical-align: -0.4em"
|
||
>3</span
|
||
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|
||
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|
||
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|
||
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|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-37-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
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|
||
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|
||
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|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-236"
|
||
><span class="msubsup" id="MathJax-Span-237"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0.958em;
|
||
height: 0px;
|
||
"
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
clip: rect(
|
||
3.365em,
|
||
1000.51em,
|
||
4.167em,
|
||
-1000em
|
||
);
|
||
top: -3.981em;
|
||
left: 0em;
|
||
"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-238"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>a</span
|
||
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|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
top: -3.831em;
|
||
left: 0.529em;
|
||
"
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-239"
|
||
style="
|
||
font-size: 70.7%;
|
||
font-family: MathJax_Main;
|
||
"
|
||
>3</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span></span></span></span></span></span></span></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-38-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-240"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-241"
|
||
><span class="msubsup" id="MathJax-Span-242"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0.958em;
|
||
height: 0px;
|
||
"
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
clip: rect(
|
||
3.365em,
|
||
1000.51em,
|
||
4.167em,
|
||
-1000em
|
||
);
|
||
top: -3.981em;
|
||
left: 0em;
|
||
"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-243"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>a</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span
|
||
><span
|
||
style="
|
||
position: absolute;
|
||
top: -3.831em;
|
||
left: 0.529em;
|
||
"
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-244"
|
||
style="
|
||
font-size: 70.7%;
|
||
font-family: MathJax_Main;
|
||
"
|
||
>3</span
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
width: 0px;
|
||
height: 3.981em;
|
||
"
|
||
></span></span></span></span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-245"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.222em;
|
||
"
|
||
>−</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-246"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.222em;
|
||
"
|
||
>2</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-247"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>=</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-248"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>1</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-39-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-249"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-250"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-251"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>s</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-40-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-252"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-253"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-254"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>s</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-41-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-255"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-256"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-257"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>t</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-42-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-258"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-259"
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-260"
|
||
style="font-family: MathJax_Main"
|
||
>1</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-261"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>≤</span
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-262"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
padding-left: 0.278em;
|
||
"
|
||
>t</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-263"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>≤</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-264"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>5000</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-43-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-265"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-266"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-267"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>t</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-44-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-268"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-269"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-270"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>i</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-45-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-271"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-272"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-273"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>s</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-46-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-274"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-275"
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-276"
|
||
style="font-family: MathJax_Main"
|
||
>1</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-277"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>≤</span
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-278"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
padding-left: 0.278em;
|
||
"
|
||
>s</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-279"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>≤</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-280"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.278em;
|
||
"
|
||
>5000</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-47-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-281"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-282"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-283"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>i</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-48-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-284"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-285"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-286"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>t</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-49-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-287"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-288"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-289"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>i</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-50-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-290"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-291"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-292"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>i</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-51-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-293"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-294"
|
||
><span
|
||
class="mi"
|
||
id="MathJax-Span-295"
|
||
style="
|
||
font-family: MathJax_Math;
|
||
font-style: italic;
|
||
"
|
||
>s</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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="#id006226366609010294"
|
||
id="id001367917703431415"
|
||
class="input-output-copier"
|
||
>
|
||
Copy
|
||
</div>
|
||
</div>
|
||
<pre id="id006226366609010294">
|
||
4
|
||
1
|
||
8
|
||
7
|
||
42
|
||
</pre
|
||
>
|
||
</div>
|
||
<div class="output">
|
||
<div class="title">
|
||
Output
|
||
<div
|
||
title="Copy"
|
||
data-clipboard-target="#id00398466806909902"
|
||
id="id007418309013542003"
|
||
class="input-output-copier"
|
||
>
|
||
Copy
|
||
</div>
|
||
</div>
|
||
<pre id="id00398466806909902">
|
||
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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-52-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-296"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-297"
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-298"
|
||
style="font-family: MathJax_Main"
|
||
>[</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-299"
|
||
style="font-family: MathJax_Main"
|
||
>1</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-300"
|
||
style="font-family: MathJax_Main"
|
||
>]</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-53-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-301"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-302"
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-303"
|
||
style="font-family: MathJax_Main"
|
||
>[</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-304"
|
||
style="font-family: MathJax_Main"
|
||
>3</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-305"
|
||
style="font-family: MathJax_Main"
|
||
>,</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-306"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.167em;
|
||
"
|
||
>4</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-307"
|
||
style="font-family: MathJax_Main"
|
||
>,</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-308"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.167em;
|
||
"
|
||
>1</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-309"
|
||
style="font-family: MathJax_Main"
|
||
>]</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-54-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-310"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-311"
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-312"
|
||
style="font-family: MathJax_Main"
|
||
>[</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-313"
|
||
style="font-family: MathJax_Main"
|
||
>1</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-314"
|
||
style="font-family: MathJax_Main"
|
||
>,</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-315"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.167em;
|
||
"
|
||
>2</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-316"
|
||
style="font-family: MathJax_Main"
|
||
>,</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-317"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.167em;
|
||
"
|
||
>4</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-318"
|
||
style="font-family: MathJax_Main"
|
||
>]</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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
|
||
><span
|
||
class="MathJax MathJax_Processed"
|
||
id="MathJax-Element-55-Frame"
|
||
tabindex="0"
|
||
style=""
|
||
><nobr
|
||
><span class="math" id="MathJax-Span-319"
|
||
><span
|
||
style="
|
||
display: inline-block;
|
||
position: relative;
|
||
width: 0em;
|
||
height: 0px;
|
||
font-size: 122%;
|
||
"
|
||
><span style="position: absolute"
|
||
><span class="mrow" id="MathJax-Span-320"
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-321"
|
||
style="font-family: MathJax_Main"
|
||
>[</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-322"
|
||
style="font-family: MathJax_Main"
|
||
>1</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-323"
|
||
style="font-family: MathJax_Main"
|
||
>,</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-324"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.167em;
|
||
"
|
||
>4</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-325"
|
||
style="font-family: MathJax_Main"
|
||
>,</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-326"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.167em;
|
||
"
|
||
>6</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-327"
|
||
style="font-family: MathJax_Main"
|
||
>,</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-328"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.167em;
|
||
"
|
||
>8</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-329"
|
||
style="font-family: MathJax_Main"
|
||
>,</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-330"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.167em;
|
||
"
|
||
>10</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-331"
|
||
style="font-family: MathJax_Main"
|
||
>,</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-332"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.167em;
|
||
"
|
||
>2</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-333"
|
||
style="font-family: MathJax_Main"
|
||
>,</span
|
||
><span
|
||
class="mn"
|
||
id="MathJax-Span-334"
|
||
style="
|
||
font-family: MathJax_Main;
|
||
padding-left: 0.167em;
|
||
"
|
||
>11</span
|
||
><span
|
||
class="mo"
|
||
id="MathJax-Span-335"
|
||
style="font-family: MathJax_Main"
|
||
>]</span
|
||
></span
|
||
></span
|
||
></span
|
||
></span
|
||
></nobr
|
||
></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/76290'
|
||
)
|
||
$('#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()
|
||
$(this)
|
||
.closest('.problemindexholder')
|
||
.find('.testCaseMarker_output_' + end)
|
||
.hide()
|
||
}
|
||
}
|
||
})
|
||
}
|
||
)
|
||
})
|
||
</script>
|
||
</div>
|
||
</div>
|
||
<br style="clear: both" />
|
||
<div id="footer">
|
||
<div>
|
||
<a href="https://codeforces.com/">Codeforces</a> (c) Copyright
|
||
2010-2025 Mike Mirzayanov
|
||
</div>
|
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<div>The only programming contests Web 2.0 platform</div>
|
||
<div>
|
||
Server time: Oct/05/2025 21:47:25<sup
|
||
title="timezone offset"
|
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style="font-size: 8px"
|
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>UTC-4</sup
|
||
>
|
||
(j2).
|
||
</div>
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<div>
|
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Desktop version, switch to
|
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<a rel="nofollow" class="switchToMobile" href="?mobile=true"
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src="//codeforces.org/s/76290/images/ton-100x100.png"
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<script type="text/javascript">
|
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$(function () {
|
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$('.switchToMobile').click(function () {
|
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Codeforces.redirect(
|
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Codeforces.updateUrlParameter(
|
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document.location.href,
|
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'mobile',
|
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'true'
|
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)
|
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)
|
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return false
|
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$('.switchToDesktop').click(function () {
|
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Codeforces.redirect(
|
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Codeforces.updateUrlParameter(
|
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document.location.href,
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'mobile',
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'false'
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$(document).ready(function () {
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if ($(window).width() < 1600) {
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$('.button-up')
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if ($(window).width() >= 1200) {
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$(window).scroll(function () {
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if ($(this).scrollTop() > 100) {
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$('.button-up').fadeIn()
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$('.button-up').fadeOut()
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$('.button-up').click(function () {
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$('body,html').animate(
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{
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scrollTop: 0
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$('.button-up').hover(
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$(this)
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.animate({
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opacity: '1'
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})
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.css({ 'background-color': '#e7ebf0', color: '#6a86a4' })
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opacity: '0.7'
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}
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)
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Codeforces.focusOnError()
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Codeforces.setCopiedToClipboardText('Copied to clipboard')
|
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|
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padding: 0.5em;
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max-height: 200px;
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overflow-y: auto;
|
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"
|
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>
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<div
|
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class="datatable"
|
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style="background-color: #e1e1e1; padding-bottom: 3px"
|
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>
|
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<div class="lt"> </div>
|
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<div class="rt"> </div>
|
||
<div class="lb"> </div>
|
||
<div class="rb"> </div>
|
||
|
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<div
|
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style="
|
||
padding: 4px 0 0 6px;
|
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font-size: 1.4rem;
|
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position: relative;
|
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"
|
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>
|
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User lists
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<div style="position: absolute; right: 0.25em; top: 0.35em">
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<span
|
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style="padding: 0; position: relative; bottom: 2px"
|
||
class="rowCount"
|
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></span>
|
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|
||
<img
|
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class="closed"
|
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src="//codeforces.org/s/76290/images/icons/control.png"
|
||
/><span class="filter" style="display: none">
|
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<img
|
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class="opened"
|
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src="//codeforces.org/s/76290/images/icons/control-270.png" /><input
|
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style="
|
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padding: 0 0 0 20px;
|
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position: relative;
|
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bottom: 2px;
|
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border: 1px solid #aaa;
|
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height: 17px;
|
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font-size: 1.3rem;
|
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"
|
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/></span>
|
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</div>
|
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</div>
|
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<div
|
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style="
|
||
background-color: white;
|
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margin: 0.3em 3px 0 3px;
|
||
position: relative;
|
||
"
|
||
>
|
||
<div class="ilt"> </div>
|
||
<div class="irt"> </div>
|
||
<table class="">
|
||
<thead>
|
||
<tr>
|
||
<th draggable="true" class="top left right">Name</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="no-items visible">
|
||
<td
|
||
style="text-align: left"
|
||
colspan="32"
|
||
class="bottom dark left right"
|
||
>
|
||
No items
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
</div>
|
||
</div>
|
||
<script type="text/javascript">
|
||
$(document).ready(function () {
|
||
// Create new ':containsIgnoreCase' selector for search
|
||
jQuery.expr[':'].containsIgnoreCase = function (a, i, m) {
|
||
return (
|
||
jQuery(a).text().toUpperCase().indexOf(m[3].toUpperCase()) >=
|
||
0
|
||
)
|
||
}
|
||
|
||
if (window.updateDatatableFilter == undefined) {
|
||
window.updateDatatableFilter = function (i) {
|
||
var parent = $(i).parent().parent().parent().parent()
|
||
$('tr.no-items', parent).remove()
|
||
$('tr', parent).hide().removeClass('visible')
|
||
var text = $(i).val()
|
||
if (text) {
|
||
$('tr' + ":containsIgnoreCase('" + text + "')", parent)
|
||
.show()
|
||
.addClass('visible')
|
||
} else {
|
||
parent.find('.rowCount').text('')
|
||
$('tr', parent).show().addClass('visible')
|
||
}
|
||
|
||
var found = false
|
||
var visibleRowCount = 0
|
||
$('tr', parent).each(function () {
|
||
if (!found) {
|
||
if ($(this).find('th').size() > 0) {
|
||
$(this).show().addClass('visible')
|
||
found = true
|
||
}
|
||
}
|
||
if ($(this).hasClass('visible')) {
|
||
visibleRowCount++
|
||
}
|
||
})
|
||
if (text) {
|
||
parent
|
||
.find('.rowCount')
|
||
.text('Matches: ' + (visibleRowCount - (found ? 1 : 0)))
|
||
}
|
||
if (visibleRowCount == (found ? 1 : 0)) {
|
||
$(
|
||
'<tr class=\'no-items visible\'><td style="text-align:left;"colspan="32">No items<\/td><\/tr>'
|
||
).appendTo($(parent).find('table'))
|
||
}
|
||
$(parent).find('tr td').removeClass('dark')
|
||
$(parent).find('tr.visible:odd td').addClass('dark')
|
||
}
|
||
|
||
$('.datatable .closed').click(function () {
|
||
var parent = $(this).parent()
|
||
$(this).hide()
|
||
$('.filter', parent).fadeIn(function () {
|
||
$('input', parent)
|
||
.val('')
|
||
.focus()
|
||
.css('border', '1px solid #aaa')
|
||
})
|
||
})
|
||
|
||
$('.datatable .opened').click(function () {
|
||
var parent = $(this).parent().parent()
|
||
$('.filter', parent).fadeOut(function () {
|
||
$('.closed', parent).show()
|
||
$('input', parent)
|
||
.val('')
|
||
.each(function () {
|
||
window.updateDatatableFilter(this)
|
||
})
|
||
})
|
||
})
|
||
|
||
$('.datatable .filter input').keyup(function (e) {
|
||
window.updateDatatableFilter(this)
|
||
e.preventDefault()
|
||
e.stopPropagation()
|
||
})
|
||
|
||
$('.datatable table').each(function () {
|
||
var found = false
|
||
$('tr', this).each(function () {
|
||
if (!found && $(this).find('th').size() == 0) {
|
||
found = true
|
||
}
|
||
})
|
||
if (!found) {
|
||
$(
|
||
'<tr class=\'no-items visible\'><td style="text-align:left;"colspan="32">No items<\/td><\/tr>'
|
||
).appendTo(this)
|
||
}
|
||
})
|
||
|
||
// Applies styles to datatables.
|
||
$('.datatable').each(function () {
|
||
$(this).find('tr:first th').addClass('top')
|
||
$(this).find('tr:last td').addClass('bottom')
|
||
$(this).find('tr:odd td').addClass('dark')
|
||
$(this)
|
||
.find('tr td:first-child, tr th:first-child')
|
||
.addClass('left')
|
||
$(this)
|
||
.find('tr td:last-child, tr th:last-child')
|
||
.addClass('right')
|
||
})
|
||
|
||
$('.datatable table.tablesorter').each(function () {
|
||
$(this).bind('sortEnd', function () {
|
||
$('.datatable').each(function () {
|
||
$(this)
|
||
.find('th, td')
|
||
.removeClass('top')
|
||
.removeClass('bottom')
|
||
.removeClass('left')
|
||
.removeClass('right')
|
||
.removeClass('dark')
|
||
$(this).find('tr:first th').addClass('top')
|
||
$(this).find('tr:last td').addClass('bottom')
|
||
$(this).find('tr:odd td').addClass('dark')
|
||
$(this)
|
||
.find('tr td:first-child, tr th:first-child')
|
||
.addClass('left')
|
||
$(this)
|
||
.find('tr td:last-child, tr th:last-child')
|
||
.addClass('right')
|
||
})
|
||
})
|
||
})
|
||
}
|
||
})
|
||
</script>
|
||
</div>
|
||
</div>
|
||
<script type="application/javascript">
|
||
$(function () {
|
||
$('.userListMarker').click(function () {
|
||
$.post(
|
||
'/data/lists',
|
||
{ action: 'findTouched' },
|
||
function (json) {
|
||
Codeforces.facebox('.userListsFacebox')
|
||
var tbody = $('#facebox tbody')
|
||
tbody.empty()
|
||
for (var i in json) {
|
||
tbody.append(
|
||
$('<tr></tr>').append(
|
||
$('<td></td>')
|
||
.attr('data-readKey', json[i].readKey)
|
||
.text(json[i].name)
|
||
)
|
||
)
|
||
}
|
||
Codeforces.updateDatatables()
|
||
tbody
|
||
.find('td')
|
||
.css('cursor', 'pointer')
|
||
.click(function () {
|
||
document.location = Codeforces.updateUrlParameter(
|
||
document.location.href,
|
||
'list',
|
||
$(this).attr('data-readKey')
|
||
)
|
||
})
|
||
},
|
||
'json'
|
||
)
|
||
})
|
||
})
|
||
</script>
|
||
</div>
|
||
<script type="application/javascript">
|
||
if (
|
||
'serviceWorker' in navigator &&
|
||
'fetch' in window &&
|
||
'caches' in window
|
||
) {
|
||
navigator.serviceWorker
|
||
.register('/service-worker-76290.js')
|
||
.then(function (registration) {
|
||
console.log('Service worker registered: ', registration)
|
||
})
|
||
.catch(function (error) {
|
||
console.log('Registration failed: ', error)
|
||
})
|
||
}
|
||
</script>
|
||
<script>
|
||
;(function () {
|
||
function c() {
|
||
var b = a.contentDocument || a.contentWindow.document
|
||
if (b) {
|
||
var d = b.createElement('script')
|
||
d.innerHTML =
|
||
"window.__CF$cv$params={r:'98a17d9be8768c96',t:'MTc1OTcxNTI0NQ=='};var a=document.createElement('script');a.src='/cdn-cgi/challenge-platform/scripts/jsd/main.js';document.getElementsByTagName('head')[0].appendChild(a);"
|
||
b.getElementsByTagName('head')[0].appendChild(d)
|
||
}
|
||
}
|
||
if (document.body) {
|
||
var a = document.createElement('iframe')
|
||
a.height = 1
|
||
a.width = 1
|
||
a.style.position = 'absolute'
|
||
a.style.top = 0
|
||
a.style.left = 0
|
||
a.style.border = 'none'
|
||
a.style.visibility = 'hidden'
|
||
document.body.appendChild(a)
|
||
if ('loading' !== document.readyState) c()
|
||
else if (window.addEventListener)
|
||
document.addEventListener('DOMContentLoaded', c)
|
||
else {
|
||
var e = document.onreadystatechange || function () {}
|
||
document.onreadystatechange = function (b) {
|
||
e(b)
|
||
'loading' !== document.readyState &&
|
||
((document.onreadystatechange = e), c())
|
||
}
|
||
}
|
||
}
|
||
})()
|
||
</script>
|
||
<iframe
|
||
height="1"
|
||
width="1"
|
||
style="
|
||
position: absolute;
|
||
top: 0px;
|
||
left: 0px;
|
||
border: medium;
|
||
visibility: hidden;
|
||
"
|
||
></iframe>
|
||
<script
|
||
defer
|
||
src="https://static.cloudflareinsights.com/beacon.min.js/vcd15cbe7772f49c399c6a5babf22c1241717689176015"
|
||
integrity="sha512-ZpsOmlRQV6y907TI0dKBHq9Md29nnaEIPlkf84rnaERnq6zvWvPUqr2ft8M1aS28oN72PdrCzSjY4U6VaAw1EQ=="
|
||
data-cf-beacon='{"version":"2024.11.0","token":"316c29dfa3804effb5a91c52a59b5bd0","server_timing":{"name":{"cfCacheStatus":true,"cfEdge":true,"cfExtPri":true,"cfL4":true,"cfOrigin":true,"cfSpeedBrain":true},"location_startswith":null}}'
|
||
crossorigin="anonymous"
|
||
></script>
|
||
<div id="datepick-div" style="display: none"></div>
|
||
<div id="cboxOverlay" style="display: none"></div>
|
||
<div
|
||
id="colorbox"
|
||
class=""
|
||
style="display: none; padding-bottom: 42px; padding-right: 42px"
|
||
>
|
||
<div id="cboxWrapper">
|
||
<div>
|
||
<div id="cboxTopLeft" style="float: left"></div>
|
||
<div id="cboxTopCenter" style="float: left"></div>
|
||
<div id="cboxTopRight" style="float: left"></div>
|
||
</div>
|
||
<div style="clear: left">
|
||
<div id="cboxMiddleLeft" style="float: left"></div>
|
||
<div id="cboxContent" style="float: left">
|
||
<div
|
||
id="cboxLoadedContent"
|
||
style="width: 0px; height: 0px; overflow: hidden; float: left"
|
||
></div>
|
||
<div id="cboxLoadingOverlay" style="float: left"></div>
|
||
<div id="cboxLoadingGraphic" style="float: left"></div>
|
||
<div id="cboxTitle" style="float: left"></div>
|
||
<div id="cboxCurrent" style="float: left"></div>
|
||
<div id="cboxNext" style="float: left"></div>
|
||
<div id="cboxPrevious" style="float: left"></div>
|
||
<div id="cboxSlideshow" style="float: left"></div>
|
||
<div id="cboxClose" style="float: left"></div>
|
||
</div>
|
||
<div id="cboxMiddleRight" style="float: left"></div>
|
||
</div>
|
||
<div style="clear: left">
|
||
<div id="cboxBottomLeft" style="float: left"></div>
|
||
<div id="cboxBottomCenter" style="float: left"></div>
|
||
<div id="cboxBottomRight" style="float: left"></div>
|
||
</div>
|
||
</div>
|
||
<div
|
||
style="
|
||
position: absolute;
|
||
width: 9999px;
|
||
visibility: hidden;
|
||
display: none;
|
||
"
|
||
></div>
|
||
</div>
|
||
<div
|
||
style="
|
||
position: absolute;
|
||
width: 0px;
|
||
height: 0px;
|
||
overflow: hidden;
|
||
padding: 0px;
|
||
border: 0px;
|
||
margin: 0px;
|
||
"
|
||
>
|
||
<div
|
||
id="MathJax_Font_Test"
|
||
style="
|
||
position: absolute;
|
||
visibility: hidden;
|
||
top: 0px;
|
||
left: 0px;
|
||
width: auto;
|
||
min-width: 0px;
|
||
max-width: none;
|
||
padding: 0px;
|
||
border: 0px;
|
||
margin: 0px;
|
||
white-space: nowrap;
|
||
text-align: left;
|
||
text-indent: 0px;
|
||
text-transform: none;
|
||
line-height: normal;
|
||
letter-spacing: normal;
|
||
word-spacing: normal;
|
||
font-size: 40px;
|
||
font-weight: normal;
|
||
font-style: normal;
|
||
font-size-adjust: none;
|
||
font-family: MathJax_Main, sans-serif;
|
||
"
|
||
></div>
|
||
</div>
|
||
</body>
|
||
</html>
|