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 whiteread::parse_line;

fn main() {
    let n: i32 = parse_line().unwrap();
    let mut c: i32 = 0;
    let mut j: i32 = 0;

    for i in  1..(n+1) {
        c = 0;
        j = (i as f64).sqrt() as i32;
        if j > 1 {
            for x in 1..j {
                for y in 1..j {
                    let k: i32 = -3*(x*x) -3*(y*y) - 2*x*y + 4*i;
                    if k > 0 {
                        let z: f64 = (((-1*(x+y)) as f64) + (k as f64).sqrt()) / 2.0;
                        if z.fract() == 0.0 && z > 0.0 {
                            c = c + 1;
                        }
                    }
                }
            }
        }
        println!("{}", c);
    }
}