Migrated from Lutece 772 Police And The Thief

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Description

There is a police and a thief in an $n\times m$ chessboard, whose initial position is $(x_p, y_p)$ and $(x_t, y_t)$. They move in turns. In each turn, one of the them must move to a neighboring grid(two grid are neighbored if they share a same edge). None of them can move out of the grid. When the police and the thief move into the same grid, the game ends and the thief was caught. Now you know the position of each other and who moves first, please figure out whether the thief would be caught if they both move wisely.

Input

In the first line, an integer $T$ is given indicating the number of test cases.

For each case, you can get two integers $n$ and $m$ in the first line. ($1\leq n,m\leq 10^3$);

The second line contain four integers $X_p,Y_p,X_t,Y_t$. ($0\leq X_p,X_t < n, 0\leq Y_p,Y_t < m$)

$(X_p, Y_p)$ is the initial position for the police, $(X_t, Y_t)$ is the initial position for the thief.

The third line contain a string police or thief，it means that which one takes the first step.

Output

For each case, output the answer (YESor NO) in a line.

Samples

1
3 3
0 1 1 2
thief

YES

Resources

第五届ACM趣味程序设计竞赛第四场（正式赛）