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)

mod stdin_reader {
  use std::io::stdin;
  use std::io::Read;

  pub struct StdinReader {
    pub buf: Vec<String>,
    pub cursor: usize,
  }

  pub fn new() -> StdinReader {
    StdinReader::new()
  }

  impl StdinReader {
    pub fn new() -> Self {
      let mut s = String::new();
      let stdin = stdin();
      stdin.lock().read_to_string(&mut s).unwrap();
      let buf = s.split_whitespace().map(|s| s.to_string()).collect();
      return StdinReader { buf: buf, cursor: 0 }
    }

    pub fn read_all(&self) -> Vec<String> {
      return self.buf.clone()
    }

    pub fn next(&mut self) -> Option<String> {
      let val = self.buf.get(self.cursor).cloned();
      self.cursor += 1;
      return val
    }

    pub fn as_i64(&mut self) -> Option<i64> {
      self.next().and_then(|s| s.parse::<i64>().ok())
    }

    pub fn as_f64(&mut self) -> Option<f64> {
      self.next().and_then(|s| s.parse::<f64>().ok())
    }

    pub fn as_usize(&mut self) -> Option<usize> {
      self.next().and_then(|s| s.parse::<usize>().ok())
    }
  }
}

fn is_int(n: f64) -> bool {
  let trunc = (n.trunc() as i64) as f64;
  return (n - trunc) < 0.0001
}

fn main() {
  let mut reader = stdin_reader::new();
  let n = reader.as_usize().unwrap();
  let d = reader.as_usize().unwrap();

  let points: Vec<Vec<f64>> = (0..n).map(|_| {
    (0..d).map(|_| reader.as_f64().unwrap()).collect()
  }).collect();

  let mut cnt = 0;
  for i in 0..n {
    for j in (i+1)..n {
      let distance = points[i].clone().into_iter().zip(points[j].clone().into_iter())
                      .map(|(l, r)| (l - r)*(l-r))
                      .fold(0.0, |sum, cur| sum + cur)
                      .sqrt();
      if is_int(distance) {
        cnt += 1
      }
    }
  }
  println!("{}", cnt);
}