You are given a grid $A$ that consists of $N$ rows and $M$ columns. Each number in the grid is either $0$ or $1$. 

Calculate the number of such triples $(i, j, h)$ where for all the pairs $(x, y)$, both $x$ and $y$ belong to $[1, h]$ if $y >= x$ and $A[i+x-1][j+y-1]$ equals to $1$. Of course, the square $(i, j, i+h-1, j+h-1)$ should be inside of this grid. In other words, calculate the count of square submatrices of the given grid $A$ which have their value equal to $1$ for every element present on and above their main diagonal.

Input format

• The first line contains an integer $T$ denoting the number of test cases.
• The first line of each testcase contains two space-separated integers $N$ and $M$ denoting the size of the grid $A$.
• The following $N$ lines describe the grid. Each line consists of $M$ characters that are either $0$ or $1$.

Output format

For each test case, print the count of square submatrices in a new line.

Constraints

$1 \le T \le 10\\ 1 \le N,M \le 3000$