题目描述

给定一张 $N×M$ 的地图，地图中有 1 个男孩，1 个女孩和 2 个鬼。

字符 . 表示道路，字符 X 表示墙，字符 M 表示男孩的位置，字符 G 表示女孩的位置，字符 Z 表示鬼的位置。

男孩每秒可以移动 3 个单位距离，女孩每秒可以移动 1 个单位距离，男孩和女孩只能朝上下左右四个方向移动。

每个鬼占据的区域每秒可以向四周扩张 2 个单位距离，并且无视墙的阻挡，也就是在第 $k$ 秒后所有与鬼的曼哈顿距离不超过 $2k$ 的位置都会被鬼占领。

注意：每一秒鬼会先扩展，扩展完毕后男孩和女孩才可以移动。

求在不进入鬼的占领区的前提下，男孩和女孩能否会合，若能会合，求出最短会合时间。

输入格式

第一行包含整数 $T$，表示共有 $T$ 组测试用例。

每组测试用例第一行包含两个整数 $N$ 和 $M$，表示地图的尺寸。

接下来 $N$ 行每行 $M$ 个字符，用来描绘整张地图的状况。（注意：地图中一定有且仅有 1 个男孩，1 个女孩和 2 个鬼）

输出格式

每个测试用例输出一个整数 $S$，表示最短会合时间。

如果无法会合则输出 $−1$。

每个结果占一行。

样例

输入：

3
5 6
XXXXXX
XZ..ZX
XXXXXX
M.G...
......
5 6
XXXXXX
XZZ..X
XXXXXX
M.....
..G...
10 10
..........
..X.......
..M.X...X.
X.........
.X..X.X.X.
.........X
..XX....X.
X....G...X
...ZX.X...
...Z..X..X

输出：

1
1
-1

数据范围与提示

$1<n,m<800$

题目源自 hdu 3085，原版题面如下：

Last night, little erriyue had a horrible nightmare. He dreamed that he and his girl friend were trapped in a big maze separately. More terribly, there are two ghosts in the maze. They will kill the people. Now little erriyue wants to know if he could find his girl friend before the ghosts find them.

You may suppose that little erriyue and his girl friend can move in 4 directions. In each second, little erriyue can move 3 steps and his girl friend can move 1 step. The ghosts are evil, every second they will divide into several parts to occupy the grids within 2 steps to them until they occupy the whole maze. You can suppose that at every second the ghosts divide firstly then the little erriyue and his girl friend start to move, and if little erriyue or his girl friend arrive at a grid with a ghost, they will die.

Note: the new ghosts also can devide as the original ghost.