----------------------
0 0 1 1 
x=1, lt=2, gt=0, remaining eq=0
2
----------------------
1 1 1 1 1 
x=1, lt=0, gt=0, remaining eq=4
1
----------------------
0 0 0 1 1 
----------------------
0 0 1 1 1 1 
x=1, lt=2, gt=0, remaining eq=2
2
----------------------
0 1 1 1 
x=1, lt=1, gt=0, remaining eq=1
1
----------------------
0 0 1 1 1 
x=1, lt=2, gt=0, remaining eq=1
2
----------------------
0 0 
----------------------
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 
x=1, lt=0, gt=0, remaining eq=17
1
----------------------
0 1 2 2 
x=1, lt=1, gt=2, remaining eq=0
2
x=2, lt=2, gt=0, remaining eq=0
4