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)

// -*- coding:utf-8-unix -*-

use proconio::input;

fn main() {
    input! {
        n: usize,
    }

    let mut ans = Vec::with_capacity(n);
    for _i in 0..n + 1 {
        ans.push(0);
    }

    for i in 1..(n as f64).sqrt() as usize {
        for j in i..(n as f64).sqrt() as usize {
            for k in j..(n as f64).sqrt() as usize {
                let value = i * i + j * j + k * k + i * j + j * k + k * i;
                // println!("{} {} {}", i, j, k);
                // println!("value: {}", value);
                if value > n {
                    continue;
                }

                if i == j && j == k {
                    ans[value as usize] += 1;
                } else if i != j && j != k && k != i {
                    ans[value as usize] += 6;
                } else {
                    ans[value as usize] += 3;
                }
            }
        }
    }

    for i in 1..n+1 {
        println!("{}", ans[i]);
    }
}