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 Kotlin (1.3.71) (judge verdict: Accepted)

fun main(args: Array<String>) {
    val n = readLine()!!.toInt()

    val ans = IntArray(n + 1) { 0 }

    for (x in 1..n) {
        if ((x * x) + (x) + 1 + (1 * x) >= n) break

        for (y in 1..n) {
            if ((x * x) + (y * y) + (x * y) + (y) + (x) >= n) break

            for (z in 1..n) {
                if ((x * x) + (y * y) + (z * z) + (x * y) + (y * z) + (z * x) > n) break

                val count = (x * x) + (y * y) + (z * z) + (x * y) + (y * z) + (z * x)
                if (count <= n) {
                    ans[count]++
                }
            }
        }
    }
    ans.takeLast(n).forEach {
        println(it)
    }
}