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.Collections;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using System.Globalization;
using System.Diagnostics;
 

class Solve
{
    public Solve() { }
    public static int Main()
    {
        new Solve().calc();
        return 0;
    }
 
 
    Scanner cin;
 
    void calc()
    {
        cin = new Scanner();
        int N = cin.nextInt();
        int D = cin.nextInt();
        int[,] array = new int[N,D];

        for (int i=0; i<N; i++)
        {
            for (int y=0; y<D; y++)
            {
                array[i, y] = cin.nextInt();
            }
        }


        int result = 0;
        for (int i=0; i<N - 1; i++)
        { 
            for (int y=i+1; y<N; y++)
            {
                double sum = 0;
                for(int num = 0; num<D; num++)
                {
                    sum += (array[i, num] - array[y, num]) * (array[i, num] - array[y, num]);
                }
                sum = Math.Sqrt(sum);
                if(sum - System.Math.Floor(sum) == 0)
                {
                    result++;
                }
            }          
        }
 
        Console.WriteLine(result);
    }
}
class Modulo
{
    private const int M = 1000000007;
    private readonly int[] m_facs;
    public int Mul(int a, int b)
    {
        return (int)(Math.BigMul(a, b) % M);
    }
    public Modulo(int n)
    {
        m_facs = new int[n + 1];
        m_facs[0] = 1;
        for (int i = 1; i <= n; ++i)
        {
            m_facs[i] = Mul(m_facs[i - 1], i);
        }
    }
    public int Fac(int n)
    {
        return m_facs[n];
    }
    public int Pow(int a, int m)
    {
        switch (m)
        {
        case 0:
            return 1;
        case 1:
            return a;
        default:
            int p1 = Pow(a, m / 2);
            int p2 = Mul(p1, p1);
            return ((m % 2) == 0) ? p2 : Mul(p2, a);
        }
    }
    public int Div(int a, int b)
    {
        return Mul(a, Pow(b, M - 2));
    }
    public int Ncr(int n, int r)
    {
        if (n < r) { return 0; }
        if (n == r) { return 1; }
        int res = Fac(n);
        res = Div(res, Fac(r));
        res = Div(res, Fac(n - r));
        return res;
    }
}
 
class Scanner
{
    string[] s;
    int i;
 
    char[] cs = new char[] { ' ' };
 
    public Scanner()
    {
        s = new string[0];
        i = 0;
    }
 
    public string next()
    {
        if (i < s.Length) return s[i++];
        string st = Console.ReadLine();
        while (st == "") st = Console.ReadLine();
        s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        if (s.Length == 0) return next();
        i = 0;
        return s[i++];
    }
 
    public int nextInt()
    {
        return int.Parse(next());
    }
    public int[] ArrayInt(int N, int add = 0)
    {
        int[] Array = new int[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextInt() + add;
        }
        return Array;
    }
 
    public long nextLong()
    {
        return long.Parse(next());
    }
 
    public long[] ArrayLong(int N, long add = 0)
    {
        long[] Array = new long[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextLong() + add;
        }
        return Array;
    }
 
    public double nextDouble()
    {
        return double.Parse(next());
    }
 
 
    public double[] ArrayDouble(int N, double add = 0)
    {
        double[] Array = new double[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextDouble() + add;
        }
        return Array;
    }
}