Consider a grid with N rows and M columns, where each cell has some integer value written in it. Every cell is connected to every side adjacent cell via an undirected edge. The cost of an edge e connecting any two cells with value a and b is $C_e = a \oplus b$. (Here $\oplus$ denotes bitwise xor of two the integers a and b)

We define a good trip between two cells $(r_1, c_1)$ and $(r_2, c_2)$ as a trip starting at cell $(r_1, c_1)$ and ending at cell $(r_2, c_2)$ while visiting every cell of the grid at least once.

There is a cost associated with every good trip. Let's say, for a given edge e, you travel that edge $T_e$ times. Then the cost of the trip is:

$\displaystyle\sum_{ \forall e}{\Bigg( C_e * \Biggl\lceil \frac{T_e}{2} \Biggr\rceil\Bigg)}$

Here, $\Big\lceil \frac{T_e}{2} \Big\rceil$ is the ceiling of the result of division of $T_e$ by 2

For the given starting cell $(r_1, c_1)$ and ending cell $(r_2, c_2)$, you have to find the minimum cost of a good trip.

Input Format

The first line will consist of the integer T denoting the number of test cases.

For each of the T test cases, the first line will consist of two integers N and M, denoting the number of rows and columns of the grid respectively.

The second line will consist of four integers, $r_1 c_1 r_2 c_2$, denoting the coordinates $(r_1, c_1)$ of the starting cell and $(r_2, c_2)$ of the ending cell.

Then, N lines will follow, each containing M integers, denoting the values in the grid, such that the $j^{th}$ value in the $i^{th}$ row will denote the number in the cell $(i, j)$ of the grid.

Output Format

For each of the T test cases, output a single integer, denoting the minimum cost of a good trip.

Constraints

$1 \le T \le 10$

$1 \le N \times M \le 10^5$

$1 \le r_1, r_2 \le N$

$1 \le c_1, c_2 \le M$

$1 \le Grid(i, j) \le 10^4$

where $Grid(i, j)$ denotes the integer in the given grid at cell $(i, j)$.