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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;

namespace ABC133B
{
    class Program
    {
        static void Main(string[] args)
        {
            var input = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();
            var N = input[0];
            var D = input[1];

            var points = new List<int[]>(D);
            for (int i = 0; i < N; i++)
                points.Add(Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray());

            var ans = 0;
            foreach (var pointPair in Permutation(points, 2))
            {
                var d = DistanceSquared(pointPair[0], pointPair[1]);
                var tmp = 0;
                if (int.TryParse(d.ToString(), out tmp))
                    ans += 1;
            }

            Console.WriteLine(ans);
        }

        static int DistanceSquared(int[] a, int[] b)
        {
            var d = 0;
            for (int i = 0; i < a.Length; i++)
            {
                var dif = b[i] - a[i];
                d += dif * dif;
            }
            return d;
        }

        static IEnumerable<int[][]> Permutation(IEnumerable<int[]> items, int k)
        {
            if (k == 1)
            {
                yield return new int[][] { items.First() };
                yield break;
            }
            foreach (var item in items)
            {
                var leftside = new int[][] { item };
                var unused = items.Except(leftside);
                foreach (var rightside in Permutation(unused, k - 1))
                    yield return leftside.Concat(rightside).ToArray();
            }
        }
    }
}