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 C (Clang 10.0.0) (judge verdict: Runtime Error)

#include<stdio.h>
#include<string.h>
#include<stdlib.h>
#include<math.h>
typedef long long ll;

int asc(const void* a, const void* b) { return *(int*)a - *(int*)b; }

int main() {
	ll n, count[10001] = {};
	scanf("%lld", &n);
	ll s = pow(n, 0.5);
	for (int i = 1; i <= s; i++) {
		for (int j = 1; j <= s; j++) {
			for (int k = 1; k <= s; k++) {
				count[i * i + j * j + k * k + i * j + j * k + k * i]++;
			}
		}
	}
	for (int i = 1; i <= n; i++)printf("%lld\n", count[i]);

	return 0;
}