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)

#![allow(non_snake_case)]

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

fn read_vec() -> Vec<i32> {
    read_line()
        .split_whitespace()
        .map(|e| e.parse().unwrap())
        .collect()
}

fn read_int_tuple() -> (i32, i32) {
    let v = read_vec();
    (v[0], v[1])
}

fn main() {
    let (N, D) = read_int_tuple();
    let N = N as usize;
    let mut coords = vec![vec![]; N];
    for i in 0..N {
        coords[i] = read_vec();
    }
    let mut ans = 0;
    for i in 0..N-1 {
        for j in i+1..N {
            let d = dist(&coords[i], &coords[j]);
            if d == (d as i32) as f64 {
                ans += 1;
            }
        }
    }
    println!("{}", ans);
}

fn dist(c1: &Vec<i32>, c2: &Vec<i32>) -> f64 {
    if c1.len() != c2.len() {
        panic!("Vectors need to have the same dimension");
    }
    let mut d = 0.0;
    for i in 0..c1.len() {
        d += (c1[i] - c2[i]).pow(2) as f64;
    }
    d.sqrt()
}