Have you ever played a game in Windows: Mine?
This game is played on a n*m board, just like the Pic(1)
On the board, Under some grids there are mines (represent by a red flag). There are numbers ‘A(i,j)’ on some grids means there’re A(i,j) mines on the 8 grids which shares a corner or a line with gird(i,j). Some grids are blank means there’re no mines on the 8 grids which shares a corner or a line with them.
At the beginning, all grids are back upward.
In each turn, Player should choose a back upward grid to click.
If he clicks a mine, Game over.
If he clicks a grid with a number on it , the grid turns over.
If he clicks a blank grid, the grid turns over, then check grids in its 8 directions.If the new grid is a blank gird or a grid with a number,it will be clicked too.
So If we click the grid with a red point in Pic(1), grids in the area be encompassed with green line will turn over.
Now Xiemao and Fanglaoshi invent a new mode of playing Mine. They have found out coordinates of all grids with mine in a game.
They also find that in a game there is no grid will turn over twice when click 2 different connected components.(In the Pic(2), grid at (1,1) will turn over twice when player clicks (0,0) and (2,2) , test data will not contain these cases).
Then, starting from Xiemao, they click the grid in turns. They both use the best strategy. Both of them will not click any grids with mine, and the one who have no grid to click is the loser.
Now give you the size of board N, M, number of mines K, and positions of every mine X
i,Y
i. Please output who will win.