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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Text;
using System.Linq;

namespace codeTester.contest190707
{
    class ProblemB
    {
        static List<long> nd = new List<long>();
        static List<List<long>> values = new List<List<long>>();
        static int answer = 0;

        public static void Main(string[] args)
        {
            Input();
            Logic();
            Output();
        }

        static void Input()
        {
            nd = ReadSpaceSeparatedValues();
            values = ReadSpaceSeparatedLists((int)nd[0]);
        }

        public static List<List<long>> ReadSpaceSeparatedLists(int n)
        {
            List<List<long>> returnValue = new List<List<long>>();
            for (int i = 0; i < n; i++)
            {
                returnValue.Add(ReadSpaceSeparatedValues());
            }
            return returnValue;
        }

        public static List<long> ReadSpaceSeparatedValues()
        {
            List<long> values = new List<long>();
            string[] inputs = Console.ReadLine().Split(' ');
            foreach (string input in inputs)
            {
                values.Add(long.Parse(input));
            }

            return values;
        }

        static void Logic()
        {
            int squareDistanceCount = 0;
            int n = (int)nd[0];
            int d = (int)nd[1];
            for (int i = 0; i < n; i++)
            {
                for(int j = i+1; j < n; j++)
                {
                    long squaredDistance = values[i]
                        .Zip(values[j], (iValue, jValue) => iValue - jValue)
                        .Aggregate((long)0, (sum, next) => sum + (next * next));

                    DebugPrint(squaredDistance.ToString());
                    if (isSquareNumber(squaredDistance))
                    {
                        squareDistanceCount++;
                    }
                }
            }
            answer = squareDistanceCount;
        }

        static bool isSquareNumber(long value)
        {
            if (value == Math.Pow(Math.Sqrt(value), 2))
            {
                return true;
            }
            return false;
        }

        static void Output()
        {
            Console.WriteLine(answer.ToString());
        }

        static void DebugPrint(string msg)
        {
            // 提出時に消す
            // Console.WriteLine(msg);
        }
    }
}