Problem:
Score : 300 points

Problem Statement

Let f(n) be the number of triples of integers (x,y,z) that satisfy both of the following conditions:

1 \leq x,y,z

x^2 + y^2 + z^2 + xy + yz + zx = n

Given an integer N, find each of f(1),f(2),f(3),\ldots,f(N).

Constraints

All values in input are integers.

1 \leq N \leq 10^4

Input

Input is given from Standard Input in the following format:

N

Output

Print N lines. The i-th line should contain the value f(i).

Sample Input 1

20

Sample Output 1

0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
3
3
0
0

For n=6, only (1,1,1) satisfies both of the conditions. Thus, f(6) = 1.

For n=11, three triples, (1,1,2), (1,2,1), and (2,1,1), satisfy both of the conditions. Thus, f(6) = 3.

For n=17, three triples, (1,2,2), (2,1,2), and (2,2,1), satisfy both of the conditions. Thus, f(17) = 3.

For n=18, three triples, (1,1,3), (1,3,1), and (3,1,1), satisfy both of the conditions. Thus, f(18) = 3.

Solution in Rust (1.42.0) (judge verdict: Accepted)

use proconio::{input, fastout};

fn main() {
  input!{
    n: i64
  }
  for i in 1..=n {
    let mut ans = 0;
      for x in 1..(n as f64).sqrt().ceil() as i64 {
          for y in x..(n as f64).sqrt().ceil() as i64 {
              for z in y..(n as f64).sqrt().ceil() as i64 {
                  if x*x + y*y + z*z + x*y + y*z + z*x == i {
                      if x == y && y == z && z == x {
                        ans += 1;
                      }else if x != y && y != z && z != x {
                        ans += 6;
                      }else{
                        ans += 3;
                      }
                  }
              }
          }
      }
    println!("{}",ans);
  }  
}