1720C · Corners

Problem: You are given a matrix consisting of $n$ rows and $m$ columns. Each cell of this matrix contains $0$ or $1$.

Let's call a square of size $2 \times 2$ without one corner cell an L-shape figure. In one operation you can take one L-shape figure, with at least one cell containing $1$ and replace all numbers in it with zeroes.

Find the maximum number of operations that you can do with the given matrix.

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

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: 101111011110
• Matrix after $1$ operation was performed: 100101011110
• Matrix after $2$ operations were performed: 100100011110
• Matrix after $3$ operations were performed: 100100010110
• Matrix after $4$ operations were performed: 100000010110
• Matrix after $5$ operations were performed: 100000010100
• Matrix after $6$ operations were performed: 100000000100
• Matrix after $7$ operations were performed: 000000000100
• Matrix after $8$ operations were performed: 000000000000

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.