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 f(x: usize, y: usize, z: usize) -> usize {
    x*x + y*y + z*z + x*y + y*z + z*x
}

#[fastout]
fn main() {
    input! {
        n: usize
    }
    let mut v = vec![0; n];
    for i in 1..n {
        if i*i > n { break; }
        for j in 1..n {
            if j*j > n { break; }
            for k in 1..n {
                if k*k > n { break; }
                let m = f(i,j,k);
                if m <= n { v[m-1] += 1; }
                else { break; }
            }
        }
    }
    for &x in &v { println!("{}", x) }
}