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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <math.h>

int main() {
    int n;
    scanf("%d", &n);
    for (int i = 1; i <= n; i++) {
        int x, y, z;
        int xx, yy, zz, xy;
        int count = 0;
        int mid = sqrt(n) + 1;
        for (x = 1; x < mid; x++) {
            xx = x * x;
            for (y = 1; y <= x; y++) {
                yy = y * y;
                xy = x * y;
                if (xx + yy >= n) {
                    break;
                }
                for (z = 1; z <= y; z++) {
                    zz = z * z;
                    if (yy + zz >= n) {
                        break;
                    }
                    if (xx + yy + zz + xy + x * z + y * z == i) {
                        if (x == y && x == z && y == z) {
                            count++;
                        } else {
                            count += 3;
                        }
                    }
                }
            }
        }
        printf("%d\n", count);
    }
    return 0;
}