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;
class Program
{
    static void Main(string[] args)
    {
            // 入力
            string[] sS = System.Console.ReadLine().Trim().Split(' ');
            int iN = int.Parse(sS[0]);
            int iD = int.Parse(sS[1]);
            List<List<int>> lstInp = new List<List<int>>();
            for (int i = 0; i < iN; i++)
            {
                sS = System.Console.ReadLine().Trim().Split(' ');
                List<int> lstRow = new List<int>();
                for (int j = 0; j < sS.Length; j++)
                {
                    lstRow.Add(int.Parse(sS[j]));
                }
                lstInp.Add(lstRow);
            }

            System.Diagnostics.Stopwatch sw = new System.Diagnostics.Stopwatch();
            sw.Start();

            // 解析
            int iOut = 0;
            for (int i = 0; i < lstInp.Count; i++)                          // A点
            {
                for (int j = i + 1; j < lstInp.Count; j++)                  // B点   A点-B点で全ての組合せ
                {
                    decimal iDis = GetDis(lstInp[i], lstInp[j]);            // A点-B点間距離
                    if (iDis - Math.Truncate(iDis) == 0) { iOut += 1; }     // 整数なら加算
                }
            }

            // 出力
            System.Console.WriteLine("{0}", iOut.ToString().Trim());

            sw.Stop();
#if DEBUG
            Console.WriteLine();
            Console.WriteLine("{0}", sw.Elapsed.ToString());
            Console.WriteLine("続行するには何かキーを押してください．．．");
            Console.ReadKey();
#endif
    }

        private static decimal GetDis(List<int> lstA, List<int> lstB)
        {
            decimal iRet = 0;
            for (int i = 0; i < lstA.Count; i++)
            {
                iRet += (decimal)Math.Pow(Math.Abs(lstA[i] - lstB[i]), 2);      // A点-B点間距離
            }
            iRet = (decimal)Math.Sqrt((double)iRet);
            return iRet;
        }

}