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 static System.Math;
using System.Linq;
using System.Text;
 
class DandA {
    static void Main(string[] args) {
        int[] nd = ReadLineIntArray();
        int[][] x = new int[nd[0]][];
        for (int i = 0; i < nd[0]; i++)
        {
            x[i] = Console.ReadLine().Split().Select(int.Parse).ToArray();
        }
        int cnt = 0;
        for (int i = 0; i < nd[0]-1; i++) {
            for (int j = i+1; j < nd[0]; j++) {
                var sum = 0.0;
                for (int k = 0; k < nd[1]; k++) {
                    sum += Math.Pow(x[i][k] - x[j][k], 2);
                }
                for (int l = 0; l <= sum; l++) {
                    if (l * l == sum) {cnt++;}
                }
            }
        }
        Console.WriteLine(cnt);
    }
 
    static string alphabet = "ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ";
    static string[] strAry = new string[] {"L", "R", "U", "D"};
    static int[] intArray = new int[10];
    static List<int> intList = new List<int>();
    static Dictionary<string, int> myTable = new Dictionary<string, int>();
    static HashSet<int>[] rtnArrAb = null;
    static HashSet<int>[] rtnArrCd = null;
    static long[,] Combi = new long[2001,2001];
    static long div = 1000000007;
  
    static private string ReadLineStr() {return Console.ReadLine();}
    static private int ReadLineInt() {return int.Parse(Console.ReadLine());}
    static private long ReadLineLong() {return long.Parse(Console.ReadLine());}
    static private double ReadLineDouble() {return double.Parse(Console.ReadLine());}
    static private string[] ReadLineStrArray() {return Console.ReadLine().Trim().Split();}
    static private int[] ReadLineIntArray() {return Console.ReadLine().Trim().Split().Select(a => int.Parse(a)).ToArray();}
    static private long[] ReadLineLongArray() {return Console.ReadLine().Trim().Split().Select(a => long.Parse(a)).ToArray();}
    static private double[] ReadLineDoubleArray() {return Console.ReadLine().Trim().Split().Select(a => double.Parse(a)).ToArray();}
    static private decimal[] ReadLineDecimalArray() {return Console.ReadLine().Trim().Split().Select(a => decimal.Parse(a)).ToArray();}
    static private List<int> ReadLineIntList() {return Console.ReadLine().Trim().Split().Select(a => int.Parse(a)).ToList();}
    static private List<long> ReadLineLongList() {return Console.ReadLine().Trim().Split().Select(a => long.Parse(a)).ToList();}
    static private string[][] ReadMLineStrArray(int arg) { return new int[arg].Select(_ => Console.ReadLine().Split()).ToArray();}
    static private int[][] ReadMLineIntArray(int arg) { return new int[arg].Select(_ => Console.ReadLine().Split().Select(int.Parse).ToArray()).ToArray();}
 
    static private bool IsPrime(int num) {
        if (num < 2) return false;
        if (num == 2) return true;
        else if (num % 2 == 0) return false;
        double sqrtNum = Math.Sqrt(num);
        for (int i = 3; i <= sqrtNum; i += 2) {
            if (num % i == 0) return false;
        }
        return true;
    }
  
    static private string IntToNString(int x, int n) {
        var nstring = "";
        var numbers = new string[] { "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "a", "b", "c", "d", "e", "f" };
        int r = 1;
        int q = x;
        while (q > 0) {
            r = q % n;
            nstring += numbers[r];
            q = q / n;
        }
        return string.Join("",nstring.Reverse());
    }
    static private long Gcd(long m,long n){
        long temp;
        while(m % n != 0) {
            temp = n;
            n = m % n;
            m = temp;
        }
        return n;
    }

    static private long Combination(long n,long r){
        if(n < r) {return 0;}
        if(n == r || r == 0) {return 1;}
        else if(Combi[n,r] == 0) {
            Combi[n,r] = (Combination(n-1,r-1)+Combination(n-1,r)) % div;
        }
        return Combi[n,r];
    }
}