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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

/*
 *  author : Atul Anand   
 *  created on : Thu Apr 02 2020
 */

import java.io.*;
import java.util.*;

public class Main{

    public static void main(String[] args) throws IOException {
        int N = in.nextInt();
        int D = in.nextInt();
        double X[][] = new double[N][D];
        for(int i = 0; i < N; i++){
            for(int j = 0; j < D; j++){
                X[i][j] = in.nextDouble();
            }
        }
        int ans = 0;
        for(int i = 0; i < N; i++){
            for(int j = i + 1; j < N; j++){
                if(IntegerDistance(X[i], X[j], D)){
                    ans++;
                }
            }
        }
        println(ans);
        in.close();
        out.close();
    }

    static boolean IntegerDistance(double a[], double b[], int D){
        double dist = 0;
        for(int i = 0; i < D; i++){
            dist += (a[i] - b[i]) * (a[i] - b[i]);
        }
        dist = Math.sqrt(dist);

        if(Math.floor(dist) == dist){
            return true;
        }

        return false;
    }

    static int MIN = Integer.MIN_VALUE;
    static int MAX = Integer.MAX_VALUE;
    static Reader in = new Reader();
    static PrintWriter out = new PrintWriter(System.out);

    static void read(int arr[], int N) throws IOException { 
    	for(int i = 0; i < N; i++){ 
    		arr[i] = in.nextInt(); 
    	} 
    }
    
    static void read(long arr[], int N) throws IOException { 
    	for(int i = 0; i < N; i++){ 
    		arr[i] = in.nextLong(); 
    	} 
    }
    
    static void read(String arr[], int N) throws IOException { 
    	for(int i = 0; i < N; i++){ 
    		arr[i] = in.next(); 
    	} 
    }
    
    static void print(Object O) {  
    	out.print(O); 
    }
    
    static void println(Object O) { 
    	out.println(O); 
    }
    
    static void println(int arr[]) { 
    	for(int i = 0; i < arr.length; i++){ 
    		print(arr[i]+" "); 
    	} 
    	println(""); 
    }

    static void println(int arr[][]) { 
    	for(int i = 0; i < arr.length; i++){ 
    		println(arr[i]); 
    	}
    }
    
    static void debug(Object O) { 
    	System.out.println(O); 
    }
}

class Reader {
    BufferedReader reader;
    StringTokenizer tokenizer;

    Reader() {
        reader = new BufferedReader(new InputStreamReader(System.in));
        tokenizer = new StringTokenizer("");
    }

    String next() throws IOException {
        while (!tokenizer.hasMoreTokens() ) { 
            tokenizer = new StringTokenizer(reader.readLine()); 
        }
        return tokenizer.nextToken();
    }

    int nextInt() throws IOException { 
        return Integer.parseInt(next()); 
    }
    
    double nextDouble() throws IOException { 
        return Double.parseDouble(next());
    }
    
    long nextLong() throws IOException { 
        return Long.parseLong(next()); 
    }
    
    String nextLine() throws IOException { 
        return reader.readLine(); 
    }
    
    void close() throws IOException { 
        reader.close(); 
    }
}