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;

fn main() {
    input!(n: u32);
    let cal = |i: u32, j: u32, k: u32| i * i + j * j + k * k + i * j + j * k + k * i;
    let mut ans = vec![0; n as usize + 1];
    for i in (1..=n).take_while(|i| i * i <= n) {
        for j in (1..=n).take_while(|j| i * i + j * j <= n) {
            for k in (1..=n).take_while(|&k| cal(i, j, k) <= n) {
                ans[cal(i, j, k) as usize] += 1;
            }
        }
    }
    for x in ans.iter().copied().skip(1) {
        println!("{}", x);
    }
}