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)

fn get_input() -> String {
    let mut word = String::new();
    std::io::stdin().read_line(&mut word).unwrap();
    word.trim().to_owned()
}

fn main() {
    let (n, d) = {
        let line = get_input();
        let mut split = line.split_whitespace();
        let n: usize = split.next().unwrap().parse().unwrap();
        let d: usize = split.next().unwrap().parse().unwrap();
        (n, d)
    };

    let mut x:Vec<Vec<i32>> = Vec::new();

    for _ in 0..n {
        let mut xn:Vec<i32> = Vec::new();
        let line = get_input();
        let mut split = line.split_whitespace();
        for _ in 0..d {
            let xnd:i32 = split.next().unwrap().parse().unwrap();
            xn.push(xnd);
        }
        x.push(xn);
    }

    let mut ans = 0;
    for i in 0..x.len()-1 {
        for j in i+1..x.len() {
            let mut total = 0;
            for yz in 0..d {
                let s = x[i][yz] - x[j][yz];
                total += s * s;
            }
            let dis = (total as f32).sqrt() as i32;
            if total == dis * dis {
                ans += 1;
            }
        }
    }
    println!("{}", ans);
}