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::{stdin, stdout, BufReader, BufRead, StdinLock, Write, BufWriter};

fn main() {
    let (std_in, std_out) = (stdin(), stdout());
    let mut br = BufReader::new(std_in.lock());
    let mut bw = BufWriter::new(std_out.lock());
    
    let tmp = rvn::<usize>(&mut br);
    let (n, d) = (tmp[0], tmp[1]);
    let mut ps = Vec::new();
    for _ in 0..n {
        ps.push(rvn::<i32>(&mut br));
    }
    let mut ans = 0;
    for i in 0..n {
        for j in i+1..n {
            let mut sq = 0;
            for k in 0..d {
                sq += (ps[i][k] - ps[j][k]) * (ps[i][k] - ps[j][k]);
            }
            for k in 1..401 {
                if k * k == sq {
                    ans += 1;
                }
            }
        }
    }
    writeln!(&mut bw, "{}", ans);
}


//////////////////////////////////////////////////////////////////////////////////
#[allow(dead_code)]
fn rs(br: &mut BufReader<StdinLock>) -> Vec<char> {
    let mut buf = String::new();
    br.read_line(&mut buf).ok();
    buf.trim().chars().collect()
}

#[allow(dead_code)]
fn rn<T: std::str::FromStr>(br: &mut BufReader<StdinLock>) -> T {
    let mut buf = String::new();
    br.read_line(&mut buf).ok();
    buf.trim().parse().ok().unwrap()
}

#[allow(dead_code)]
fn rvs(br: &mut BufReader<StdinLock>) -> Vec<Vec<char>> {
    let mut buf = String::new();
    br.read_line(&mut buf).ok();
    buf.trim().split_whitespace().map(|e| e.chars().collect()).collect()
}

#[allow(dead_code)]
fn rvn<T: std::str::FromStr>(br: &mut BufReader<StdinLock>) -> Vec<T> {
    let mut buf = String::new();
    br.read_line(&mut buf).ok();
    buf.trim().split_whitespace().map(|e| e.parse().ok().unwrap()).collect()
}