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(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
#[allow(unused_imports)]
use std::io::prelude::BufRead;
#[allow(unused_imports)]
use std::io::{stdin, stdout, BufReader, BufWriter, Write};
#[allow(unused_imports)]
use std::mem::swap;
#[allow(unused_imports)]
use std::str::FromStr;

fn main() {
	let line = read_vector::<usize>();
	let (n, d) = (line[0], line[1]);
	let coords = read_matrix::<i64>();
	let mut ans = 0;
	for i in 0..n {
		for j in (i + 1)..n {
			let dist_2 = (0..d).fold(0, |acc, k| acc + (coords[i][k] - coords[j][k]).pow(2));
			let root = (dist_2 as f64).sqrt() as i64;
			if root.pow(2) == dist_2 {
				ans += 1;
			}
		}
	}
	println!("{}", ans);
}


#[allow(dead_code)]
fn read<T>() -> T where T: std::str::FromStr, T::Err: std::fmt::Debug {
    let mut buf = String::new();
    stdin().read_line(&mut buf).unwrap();
    return buf
        .trim()
        .parse()
        .unwrap();
}

#[allow(dead_code)]
fn read_vector<T>() -> Vec<T> where T: std::str::FromStr, T::Err: std::fmt::Debug {
    let mut buf = String::new();
    stdin().read_line(&mut buf).unwrap();
    return buf
        .split_whitespace()
        .map(|s| s.parse().unwrap())
        .collect();
}

#[allow(dead_code)]
fn read_matrix<T>() -> Vec<Vec<T>> where T: std::str::FromStr, T::Err: std::fmt::Debug {
    use std::io::prelude::*;
    let stdin = stdin();
    return stdin
        .lock()
        .lines()
        .map(|line| line
            .unwrap()
            .split_whitespace()
            .map(|s| s.parse().unwrap())
            .collect())
        .collect();
}