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 main() {
    #[allow(unused_imports)]
    use std::io::{Read, Write, BufWriter};
    let mut a = Vec::new();
    std::io::stdin().read_to_end(&mut a).unwrap();
    let a = String::from_utf8(a).unwrap();
    let mut a = a.split_whitespace();
    #[allow(unused_mut,unused_variables)]
    let mut b = BufWriter::new(std::io::stdout());
    macro_rules! yomu { () => (a.next().unwrap().parse().unwrap()) }
    #[allow(unused_macros)]
    macro_rules! kaku { ($($arg:tt)*) => (writeln!(b, $($arg)*).unwrap()) }
    #[allow(unused_imports)]
    use std::cmp::{min, max};

    let n: usize = yomu!();
    let d: usize = yomu!();
    let mut xs: Vec<Vec<i32>> = vec![vec![0; d]; n];
    for i in 0..n {
        for j in 0..d {
            xs[i][j] = yomu!();
        }
    }
    let mut ans = 0;
    for i in 0..n {
        for j in 0..i {
            let mut s = 0;
            for k in 0..d {
                s += (xs[i][k] - xs[j][k]) * (xs[i][k] - xs[j][k]);
            }
            let t = (s as f64).sqrt() as i32;
            if t * t == s {
                ans += 1;
            }
        }
    }
    println!("{}", ans);
}