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;

class Program
{
    static string InputPattern = "InputX";

    static List<string> GetInputList()
    {
        var WillReturn = new List<string>();

        if (InputPattern == "Input1") {
            WillReturn.Add("3 2");
            WillReturn.Add("1 2");
            WillReturn.Add("5 5");
            WillReturn.Add("-2 8");
            //1
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("3 4");
            WillReturn.Add("-3 7 8 2");
            WillReturn.Add("-12 1 10 2");
            WillReturn.Add("-2 8 9 3");
            //2
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("5 1");
            WillReturn.Add("1");
            WillReturn.Add("2");
            WillReturn.Add("3");
            WillReturn.Add("4");
            WillReturn.Add("5");
            //10
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    static void Main()
    {
        List<string> InputList = GetInputList();

        var XArrList = new List<int[]>();

        foreach (string EachStr in InputList.Skip(1)) {
            XArrList.Add(EachStr.Split(' ').Select(X => int.Parse(X)).ToArray());
        }

        int Answer = 0;
        for (int I = 0; I <= XArrList.Count - 1; I++) {
            for (int J = I + 1; J <= XArrList.Count - 1; J++) {
                if (IsOkPair(XArrList[I], XArrList[J])) {
                    Answer++;
                }
            }
        }
        Console.WriteLine(Answer);
    }

    //配列のペアを引数として、
    static bool IsOkPair(int[] PArr1, int[] PArr2)
    {
        long SumVal = 0;
        for (int I = 0; I <= PArr1.GetUpperBound(0); I++) {
            SumVal += (PArr1[I] - PArr2[I]) * (PArr1[I] - PArr2[I]);
        }
        return IsHeihouSuu(SumVal);
    }

    //2分法で平方数かの判定
    static bool IsHeihouSuu(long pVal)
    {
        long LeftP = 0;
        long RightP = pVal;
        long MidP;

        while (LeftP <= RightP) {
            MidP = (LeftP + RightP) / 2;
            //Console.WriteLine("探索対象={0},LeftP={1},MidP={2},RightP={3}", pVal, LeftP, MidP, RightP);
            long NijyouVal = MidP * MidP;
            if (NijyouVal == pVal) return true;
            if (NijyouVal > pVal) {
                RightP = MidP - 1;
            }
            else {
                LeftP = MidP + 1;
            }
        }
        return false;
    }
}