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 Rust (1.15.1) (judge verdict: Accepted)

use std::io;

fn main() {
	let mut buf = String::new();
	io::stdin().read_line(&mut buf).expect("");
	let mut iter = buf.split_whitespace();
	let n = iter.next().unwrap().parse::<i32>().ok().unwrap();
	let d = iter.next().unwrap().parse::<i32>().ok().unwrap();
	let mut v :Vec<Vec<i32>> = Vec::new();
	for i in 0..n {
		v.push(Vec::new());
		let mut buf = String::new();
		io::stdin().read_line(&mut buf).expect("");
		let mut iter = buf.split_whitespace();
		for j in iter {
			v[i as usize].push(j.parse::<i32>().ok().unwrap());
		}
	}
	
	let mut cnt = 0;
	for i in 0..n {
		for j in (i+1)..n {
			let mut dis:i32 = 0;
			for k in 0..d {
				dis += (v[ j as usize][k as usize] - v[i as usize][k as usize])*(v[j as usize][k as usize] - v[i as usize][k as usize]);
			}
			let mut k = 0;
			while(k <= dis){
				if k*k == dis {
					cnt += 1;
					break;
				}
				k += 1;
			}
		}
	}
	println!("{}", cnt);
}