Score : 700 points
Snuke is playing a puzzle game. In this game, you are given a rectangular board of dimensions R × C, filled with numbers. Each integer i from 1 through N is written twice, at the coordinates (x_{i,1},y_{i,1}) and (x_{i,2},y_{i,2}).
The objective is to draw a curve connecting the pair of points where the same integer is written, for every integer from 1 through N. Here, the curves may not go outside the board or cross each other.
Determine whether this is possible.
Input is given from Standard Input in the following format:
R C N x_{1,1} y_{1,1} x_{1,2} y_{1,2} : x_{N,1} y_{N,1} x_{N,2} y_{N,2}
Print YES
if the objective is achievable; print NO
otherwise.
4 2 3 0 1 3 1 1 1 4 1 2 0 2 2
YES
The above figure shows a possible solution.
2 2 4 0 0 2 2 2 0 0 1 0 2 1 2 1 1 2 1
NO
5 5 7 0 0 2 4 2 3 4 5 3 5 5 2 5 5 5 4 0 3 5 1 2 2 4 4 0 5 4 1
YES
1 1 2 0 0 1 1 1 0 0 1
NO