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 std::io::stdin;
use std::str::FromStr;

fn main(){
    let n: usize = get_one();
    let mut ans = vec![0; n+1];
    for x in 1..101 {
        for y in 1..101 {
            for z in 1..101 {
                let f = x*x + y*y + z*z +
                    x*y + y*z + z*x;
                if f <= n {
                    ans[f] += 1
                }
            }
        }
    }
    for i in 1..n+1 {
        println!("{}", ans[i]);
    }
}

#[allow(dead_code)]
fn get_line() -> String {
    let mut s = String::new();
    match stdin().read_line(&mut s){
        Ok(_) => {s.trim().to_string()}
        Err(_) => String::new()
    }
}

#[allow(dead_code)]
fn get_vec<T: std::str::FromStr>() -> Vec<T> {
    let line = get_line();
    line.split_whitespace().filter_map(|x| x.parse().ok()).collect()
}

#[allow(dead_code)]
fn get_one<T: FromStr + Copy>() -> T {
    let v = get_vec();
    v[0]
}

#[allow(dead_code)]
fn get_pair<T: FromStr + Copy>() -> (T, T) {
    let v = get_vec();
    (v[0], v[1])
}

#[allow(dead_code)]
fn get_triple<T: FromStr + Copy>() -> (T, T, T) {
    let v = get_vec();
    (v[0], v[1], v[2])
}

#[allow(dead_code)]
fn get_chars() -> Vec<char> {
    get_line().chars().collect()
}

#[allow(dead_code)]
fn vec_min(xs: &Vec<i64>) -> i64 {
    xs.iter().map(|&x|x).fold(std::i64::MAX, std::cmp::min)
}

#[allow(dead_code)]
fn vec_max(xs: &Vec<i64>) -> i64 {
    xs.iter().map(|&x|x).fold(std::i64::MIN, std::cmp::max)
}

#[allow(dead_code)]
fn vec_sum(xs: &Vec<i64>) -> i64 {
    xs.iter().fold(0, |acc, &x| acc+x)
}