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.

Examples

Input

3 2
1 2
5 5
-2 8


Output

1


Input

3 4
-3 7 8 2
-12 1 10 2
-2 8 9 3


Output

2


Input

5 1
1
2
3
4
5


Output

10
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
    	
		Scanner sc = new Scanner(System.in);
		// 整数の入力
		int N = sc.nextInt();
		int D = sc.nextInt();
		
		int intArray[][] = new int[N][D];

		for(int i = 0 ;i < N;i++){
			for(int j = 0 ;j < D;j++){
				intArray[i][j] = sc.nextInt();
			}
		}

		int cnt = 0;
		for(int i = 0 ;i < N-1;i++){
			for(int i2 = i+1 ;i2 < N;i2++){
				int sum = 0;
				for(int j = 0 ;j < D;j++){
					sum += (int) Math.pow(Math.abs(intArray[i][j]-intArray[i2][j]),2);
				}
				int sumd = (int)Math.round(Math.sqrt(sum));
				if(sum == Math.pow(sumd, 2)) {
					cnt ++;
				}
//			String st = String.valueOf(sumd);
//			if(st.matches( "^(0|[-]?[1-9][0-9]*)$" )) {
//				cnt ++;
//			};
			}
		}

		System.out.println(cnt);

   		sc.close();
        return ;

    }
    
}

