Green Boy Can't You Solve It Out? Ep. 2
1 problem for div3 participants.
Beautiful Dice Painting
When Epis is bored, she will draw dices.
The canvas contains n*n dots. Initially they are all white. You need to paint exactly v dots black so that the final canvas is central symmetric. The canvas is central symmetric if and only if for all pairs of locations (i,j) (k,l) such that i+k=l+j=n+1, the color of (i,j) is the same as the color of (k,l).
For example, when n=3,v=3, here are some possible drawings:
WBW WBW WBW
BWW WBW WWB
Now you are given v. Find the smallest n that could have the dice painted and show a possible approach. If there are many approaches, print any.
2 BW WB
3 BWB BWB BWB
5 BBWBB WWBWW WWBWW WWBWW BBWBB
It can be proven that n=4 will not work.
1\leq v\leq 10^6
If we have already known n, then you can only consider a half of the grid... You can draw whatever you like!
If n=\left\lceil\sqrt v\right\rceil doesn't work, try n+1! At least one of them will work.
来源：Hell Hole Studios Blog