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)

#[allow(unused_imports)]
use proconio::marker::{Bytes, Chars};
use proconio::{fastout, input};
#[fastout]
fn main() {
    input! {
        n: usize,
    }
    let mut ans = vec![0; n];
    for i in 1..n {
        for j in 1..i + 1 {
            'inner: for k in 1..j + 1 {
                let tmp = (i + j + k) * (i + j + k) - (i * j + j * k + k * i);
                if tmp > n {
                    break 'inner;
                } else {
                    if i == j && i == k {
                        ans[tmp - 1] += 1;
                    } else if i != j && j != k && k != i {
                        ans[tmp - 1] += 6;
                    } else {
                        ans[tmp - 1] += 3;
                    }
                }
            }
        }
    }
    for i in 0..n {
        println!("{:?}", ans[i]);
    }
}