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.Text;
using System.Collections.Generic;
using System.ComponentModel;
using System.Linq;
using System.Threading.Tasks;
class Program
{
	static void Main(string[] args)
	{
		var input = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();
		int N = input[0];
		int D = input[1];
		double[,] P = new double[N, D];
        for(var i = 0; i < N; i++)
		{
			var inputer = Console.ReadLine().Split().Select(x => double.Parse(x)).ToArray();
            for(var j = 0; j < D; j++)
			{
				P[i, j] = inputer[j];
			}
		}

		List<double> dis = new List<double>();
        
        for(var i = 0; i < N - 1; i++)
		{
			
            for(var j = i + 1; j < N; j++)
			{
				double d = 0;
              for(var k = 0; k < D; k++)
				{
					d += (P[i, k] - P[j, k]) * (P[i, k] - P[j, k]);
				}
				dis.Add(Math.Sqrt(d));
			}
		}
		int cnt = 0;
        for(var i = 0; i < dis.Count; i++)
		{
			int disa = (int)dis[i];
			if (dis[i] - disa == 0)
			{
				cnt++;
			}
		}
		Console.WriteLine(cnt);


	}
}

//var input = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();
//入力用

public class Calculation //各種値の計算メソッド
{
	public int GetGcd(int a, int b) //最大公約数(２数)
	{
		if (a * b == 0)
		{
			return 0;
		}
		if (a < b)
		{
			int c = a;
			a = b;
			b = c;
		}

		int r = a % b;
		while (r > 0)
		{
			a = b;
			b = r;
			r = a % b;
		}
		return b;
	}
	public int GetGcdOfSortedArray(int[] array) //最大公約数(ソート済み数列)
	{
		if (array.Length == 0) { return 1; }
		else if (array.Length == 1) { return array[0]; }
		else
		{
			int n = 0;
			int g = -1;
			while (n <= array.Length - 2)
			{

				int a = array[n + 1];
				int b = array[n];
				int r = a % b;
				while (r > 0)
				{
					a = b;
					b = r;
					r = a % b;
				}
				g = b;
				array[n + 1] = g;
				n++;
			}

			return g;

		}
	}
	public long GetGcdOfSortedArrayL(long[] array) //最大公約数(ソート済み配列[long型])
	{
		if (array.Length == 0) { return 1; }
		else if (array.Length == 1) { return array[0]; }
		else
		{
			int n = 0;
			long g = -1;
			while (n <= array.Length - 2)
			{

				long a = array[n + 1];
				long b = array[n];
				long r = a % b;
				while (r > 0)
				{
					a = b;
					b = r;
					r = a % b;
				}
				g = b;
				array[n + 1] = g;
				n++;
			}

			return g;

		}
	}

	public long GetNCR(int n, int r) //二項係数(生の値)
	{
		if (n == 1) { return 1; }
		long[] nC = new long[n + 1];
		nC[0] = 1;
		for (var i = 0; i <= r - 1; i++)
		{
			nC[i + 1] = nC[i] * (n - i) / (i + 1);
		}
		return nC[r];
	}


}

class Modulo //1000000007で割る問題用
{
	private const int M = 1000000007;
	private readonly int[] m_facs;
	public int Mul(int a, int b) //掛け算
	{
		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) //累乗
	{
		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) //除算
	{
		return Mul(a, Pow(b, M - 2));
	}
	public int Ncr(int n, int r) //二項係数
	{
		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;
	}
	public Modulo() { }
}