CF1797A.Li Hua and Maze

There is a rectangular maze of size $n\times m$. Denote $(r,c)$ as the cell on the $r$-th row from the top and the $c$-th column from the left. Two cells are adjacent if they share an edge. A path is a sequence of adjacent empty cells.

Each cell is initially empty. Li Hua can choose some cells (except $(x_1, y_1)$ and $(x_2, y_2)$) and place an obstacle in each of them. He wants to know the minimum number of obstacles needed to be placed so that there isn't a path from $(x_1, y_1)$ to $(x_2, y_2)$.

Suppose you were Li Hua, please solve this problem.

有一个大小为 $n\times m$ 的矩形迷宫。记 $(r,c)$ 表示从上往下数第 $r$ 行、从左往右数第 $c$ 列的格子。若两个格子共享一条边，则称它们相邻。一条路径是指一系列相邻的空格子组成的序列。

每个格子初始均为空。李华可以选择若干个格子（但不能选 $(x_1, y_1)$ 和 $(x_2, y_2)$）并在其中各放置一个障碍物。他想知道：为使得从 $(x_1, y_1)$ 到 $(x_2, y_2)$ 不存在任何路径，所需放置的障碍物的最少数量是多少？

假设你是李华，请解决此问题。

The first line contains the single integer $t$ ($1 \le t \le 500$) — the number of test cases.

The first line of each test case contains two integers $n,m$ ($4\le n,m\le 10^9$) — the size of the maze.

The second line of each test case contains four integers $x_1,y_1,x_2,y_2$ ($1\le x_1,x_2\le n, 1\le y_1,y_2\le m$) — the coordinates of the start and the end.

It is guaranteed that $|x_1-x_2|+|y_1-y_2|\ge 2$.

第一行包含一个整数 $t$（$1 \le t \le 500$）——测试用例的数量。

每个测试用例的第一行包含两个整数 $n,m$（$4\le n,m\le 10^9$）——迷宫的尺寸。

每个测试用例的第二行包含四个整数 $x_1,y_1,x_2,y_2$（$1\le x_1,x_2\le n,\ 1\le y_1,y_2\le m$）——起点和终点的坐标。

保证 $|x_1-x_2|+|y_1-y_2|\ge 2$。

For each test case print the minimum number of obstacles you need to put on the field so that there is no path from $(x_1, y_1)$ to $(x_2, y_2)$.

对于每个测试用例，输出需要在场地上放置的障碍物的最少数量，使得从 $(x_1, y_1)$ 到 $(x_2, y_2)$ 不存在路径。

In test case 1, you can put obstacles on $(1,3), (2,3), (3,2), (4,2)$. Then the path from $(2,2)$ to $(3,3)$ will not exist.

在测试用例 1 中，你可以在格子 $(1,3)$、$(2,3)$、$(3,2)$ 和 $(4,2)$ 上放置障碍物。此时，从 $(2,2)$ 到 $(3,3)$ 的路径将不存在。