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 JavaScript (Node.js 12.16.1) (judge verdict: Wrong Answer)

console.log((args=>{
  const N = args.trim()|0;
  const a = Array(N).fill(0);
  for ( let x = 1; x*(x+2)+2 < N; x++ ) {
    for ( let y = 1; y*(y+2)+2 < N; y++ ) {
      for ( let z = 1; z*(z+2)+2 < N; z++ ) {
        const i = x*x + y*y + z*z + x*y + y*z + z*x;
        if ( i >= N ) break;
        a[i-1]++;
      }
    }
  }
  return a.join`\n`;
})(require('fs').readFileSync('/dev/stdin', 'utf8')));