Rain loves triangles, especially equilateral ones. Thus, Rain has $N$ points in $M$-dimensional space where each coordinate point is either $0$ or $1$, and he wants you to calculate the number of equilateral triangles with vertices on the points. The distance between two points is the usual Euclidean distance.

The Euclidean distance between points $a=(a_1,a_2,\dots ,a_M),b=(b_1,b_2,\dots ,b_M)$ is $\sqrt{(a_1-b_1{)}^2+(a_2-b_2{)}^2+\cdots +(a_M-b_M{)}^2}$.

Constraints

The points are pairwise-distinct.

$1\le N\le 400$

$1\le M\le 5\times {10}^4$

$a_{ij}\in \{0,1\}$

Subtask 1 [80%]

$1\le N,M\le 400$

Subtask 2 [20%]

No additional constraints.

Input Specification

The first line contains two integers $N$ and $M$.

The next $N$ lines each represent a point $a_i$. Each line has $M$ integers $a_{i1},\dots ,a_{iM}$, representing the coordinates of the point.

Output Specification

Output the number of equilateral triangles where each vertex is a given point.

Sample Input

4 3
0 0 1
1 0 0
0 1 0
0 1 1

Sample Output

1

Explanation for Sample

Only the first $3$ points form an equilateral triangle.