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 \((i, j)\).