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::{fastout, input};

fn main() {
    input! {
        n: i64,
    };
    let max: i64 = (n as f64).sqrt().ceil() as i64;
    let mut f_vec: Vec<usize> = vec![0; n as usize];
    for x in 1..=max {
        for y in x..=max {
            for z in y..=max {
                let temp = (x + y + z) * (x + y + z) - x * y - y * z - z * x;
                if temp > n {
                    continue;
                }
                if x == y && x == z {
                    f_vec[temp as usize - 1] += 1;
                } else if x == y || y == z {
                    f_vec[temp as usize - 1] += 3;
                } else {
                    f_vec[temp as usize - 1] += 6;
                }
            }
        }
    }
    f_vec.iter().for_each(|f| println!("{}", f));
}