Description

Input

The first line contains one integer $t$ ($1 \leq t \leq 500$) — the number of test cases. Then follow the descriptions of each test case.

The first line of each test case contains two integers $n$ and $m$ ($2 \leq n, m \leq 500$) — the size of the matrix.

Each of the following $n$ lines contains a binary string of length $m$ — the description of the matrix.

It is guaranteed that the sum of $n$ and the sum of $m$ over all test cases does not exceed $1000$.

Output

For each test case output the maximum number of operations you can do with the given matrix.

4
4 3
101
111
011
110
3 4
1110
0111
0111
2 2
00
00
2 2
11
11
 
 
 
 
 
 
 
 

8
9
0
2

Note

In the first testcase one of the optimal sequences of operations is the following (bold font shows l-shape figure on which operation was performed):

• Matrix before any operation was performed:

  1	0	1
  1	1	1
  0	1	1
  1	1	0

• Matrix after $1$ operation was performed:

  1	0	0
  1	0	1
  0	1	1
  1	1	0

• Matrix after $2$ operations were performed:

  1	0	0
  1	0	0
  0	1	1
  1	1	0

• Matrix after $3$ operations were performed:

  1	0	0
  1	0	0
  0	1	0
  1	1	0

• Matrix after $4$ operations were performed:

  1	0	0
  0	0	0
  0	1	0
  1	1	0

• Matrix after $5$ operations were performed:

  1	0	0
  0	0	0
  0	1	0
  1	0	0

• Matrix after $6$ operations were performed:

  1	0	0
  0	0	0
  0	0	0
  1	0	0

• Matrix after $7$ operations were performed:

  0	0	0
  0	0	0
  0	0	0
  1	0	0

• Matrix after $8$ operations were performed:

  0	0	0
  0	0	0
  0	0	0
  0	0	0

In the third testcase from the sample we can not perform any operation because the matrix doesn't contain any ones.

In the fourth testcase it does not matter which L-shape figure we pick in our first operation. We will always be left with single one. So we will perform $2$ operations.