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.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder_20190707_1
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] input1 = Console.ReadLine().Split(' ');
            int dotsCount = int.Parse(input1[0]);
            int dimension = int.Parse(input1[1]);

            List<string[]> dots = new List<string[]>();

            for(int i = 0; i < dotsCount; i++)
            {
                dots.Add(Console.ReadLine().Split(' '));
            }

            int answer = 0;

            for(int i = 0; i < dots.Count; i++)
            {
                for (int j = 0; j < dots.Count; j++)
                {
                    string[] dotsX;
                    string[] dotsY;

                    if (i == j)
                    {
                        continue;
                    }
                    else
                    {
                        dotsX = dots[i];
                        dotsY = dots[j];
                    }

                    double distance = 0;

                    for (int k = 0; k < dimension; k++)
                    {
                        distance += Math.Pow(int.Parse(dotsX[k]) - int.Parse(dotsY[k]), 2);
                    }

                    distance = Math.Sqrt(distance);

                    if (distance - Math.Floor(distance) == 0)
                    {
                        answer++;
                    }
                }
            }

            Console.WriteLine((answer / 2).ToString());
        }
    }
}