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;
use std::collections::HashMap;

fn read_line() -> String {
    let mut line = String::new();

    io::stdin().read_line(&mut line)
        .expect("Failed to read line");
    return line;
}
fn to_i(s: &str) -> i64 {
    return s.trim().parse()
        .expect("Please type a number!");
}
fn read_nums() -> Vec<i64>
{
    let line = read_line();
    let items: Vec<&str> = line.split(' ').collect();

    let mut nums: Vec<i64> = Vec::new();

    for item in items {
        nums.push(to_i(item));
    }
    return nums;
}
fn dist(aa: &Vec<i64>, bb: &Vec<i64>) -> f64
{
    let mut ret = 0.0;
    let n = aa.len();
    for i in 0..n {
        let index = i as usize;
        let a = aa[index];
        let b = bb[index];
        let d = (a-b)*(a-b);
        ret += d as f64;
    }
    ret = ret.sqrt();
    return ret;
}

fn main() {
    //println!("start");
    let nd = read_nums();
    let n = nd[0];
    let d = nd[1];
   
    let mut vv: Vec<Vec<i64>> = Vec::new();
    for i in 0..n {
        let v = read_nums();
        vv.push(v);
    }
    let mut count = 0;
    for i in 0..n {
        for j in i+1..n {
            let d = dist(&vv[i as usize], &vv[j as usize]);
            let d2 = d.floor();
            if d2 == d {
                count += 1;
            }
        }
    }
    //println!("{}",n);
    let ret = count;
 
    print!("{}", ret);
    
    
}