Problem Statement

There are $N$ points in a $D$-dimensional space.

The coordinates of the $i$-th point are $(X_{i1}, X_{i2}, ..., X_{iD})$.

The distance between two points with coordinates $(y_1, y_2, ..., y_D)$ and $(z_1, z_2, ..., z_D)$ is $\sqrt{(y_1 - z_1)^2 + (y_2 - z_2)^2 + ... + (y_D - z_D)^2}$.

How many pairs $(i, j)$ $(i < j)$ are there such that the distance between the $i$-th point and the $j$-th point is an integer?

Constraints

• All values in input are integers.
• $2 \leq N \leq 10$
• $1 \leq D \leq 10$
• $-20 \leq X_{ij} \leq 20$
• No two given points have the same coordinates. That is, if $i \neq j$, there exists $k$ such that $X_{ik} \neq X_{jk}$.

Input

Input is given from Standard Input in the following format:

N D
X_{11} X_{12} ... X_{1D}
X_{21} X_{22} ... X_{2D}
\vdots
X_{N1} X_{N2} ... X_{ND}

Output

Print the number of pairs $(i, j)$ $(i < j)$ such that the distance between the $i$-th point and the $j$-th point is an integer.