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: Time Limit Exceeded)

fn main() {
    proconio::input! {
        n: usize,
    }
    for i in 0..n {
        println!("{}", f(i + 1));
    }
}

fn f(n: usize) -> u64 {
    let mut r = 0;
    let mut x = 1;
    while x <= n {
        let mut y = x;
        while y <= n {
            if x * x + y * y + 1 + x * y + y + x <= n {
                let mut z = y;
                while x * x + y * y + z * z + x * y + y * z + z * x < n {
                    z += 1;
                }
                if x * x + y * y + z * z + x * y + y * z + z * x == n {
                    if x == y && y == z {
                        r += 1;
                    } else if x == y && y == z {
                        r += 2;
                    } else {
                        r += 3;
                    }
                }
            }
            y += 1;
        }
        x += 1;
    }
    r
}