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)

use proconio::input;

fn main() {
    input! {
        n: i64,
    }

    for num in 1..n + 1 {
        let mut count = 0;

        'outer: for x in 1..=num {
            for y in x..=num {
                for z in y..=num {
                    let this = (x + y + z) * (x + y + z);
                    if this == num + x * y + y * z + z * x {
                        count += 3;
                        if x == y && x == z {
                            count -= 2;
                        }
                        break 'outer;
                    }
                    if this > num + x * y + y * z + z * x {
                        break;
                    }
                }
            }
        }
        println!("{}", count);
    }
}