Problem:
Score : 200 points

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.

Sample Input 1

3 2
1 2
5 5
-2 8

Sample Output 1

1

The number of pairs with an integer distance is one, as follows:

The distance between the first point and the second point is \sqrt{|1-5|^2 + |2-5|^2} = 5, which is an integer.

The distance between the second point and the third point is \sqrt{|5-(-2)|^2 + |5-8|^2} = \sqrt{58}, which is not an integer.

The distance between the third point and the first point is \sqrt{|-2-1|^2+|8-2|^2} = 3\sqrt{5}, which is not an integer.

Sample Input 2

3 4
-3 7 8 2
-12 1 10 2
-2 8 9 3

Sample Output 2

2

Sample Input 3

5 1
1
2
3
4
5

Sample Output 3

10

Solution in Python (3.4.3) (judge verdict: Accepted)

import bisect
import sys
import math

verbose = False


def get_iv():
    args = sys.stdin.readline()
    argv = args.split()
    iargv = [int(arg) for arg in argv]
    return iargv


def get_fv():
    args = sys.stdin.readline()
    argv = args.split()
    iargv = [float(arg) for arg in argv]
    return iargv


def calc_dist(Lhs, Rhs):
    dist = 0
    for off in range(len(Lhs)):
        dx = Lhs[off] - Rhs[off]
        dist += dx * dx
    dist = math.sqrt(dist)
    return dist


def is_int(fl):
    ifl = int(fl + .5)
    df = abs(ifl - fl)
    return df < 1e-4


def num_sqare(N, X):
    rv = 0
    for i in range(N):
        for j in range(i + 1, N):
            dist = calc_dist(X[i], X[j])
            if is_int(dist):
                rv += 1
    return rv


def main():
    specs = get_iv()
    N = specs[0]
    D = specs[1]
    X = []
    for i in range(N):
        v = get_iv()
        X.append(v)
    rv = num_sqare(N, X)
    print(rv)


if __name__ == '__main__':
    main()
    # mock()