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: Accepted)

    using System;
    using System.Linq;
    using System.Collections.Generic;
    using static System.Console;
    using System.Text;
     
     
    namespace AtCoder_Beginner_Contest_132
    {
        class Program
        {
            static public long[] Sarray() { return ReadLine().Split().Select(long.Parse).ToArray(); }
            static public List<long> Slist() { return ReadLine().Split().Select(long.Parse).ToList(); }
            static void Main(string[] args)
            {
                var ND=Sarray();
                var N = ND[0];
                var D = ND[1];
                var Xij = new List<long>[N];
                for(var i=0;i<N;++i)
                {
                    Xij[i] = Slist();
                }
                var cnt = 0;
                for(var i=0;i<N;++i)
                {
                    for(var j=i+1;j<N;++j)
                    {
                        var sum = 0L;
                        for (var k = 0; k < D;++k)
                        {
                            sum += (long)Math.Pow(Xij[i][k] - Xij[j][k], 2);
                        }
                        if (Math.Sqrt(sum) - (long)Math.Sqrt(sum) < 0.000001)
                            ++cnt;
                    }
                }
                WriteLine(cnt);
            }
        }
    }