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){0}

    for (x in 1..n) {
        if (x*x + 2*x > n) break
        y@for (y in 1..n) {
            if (x*x + y*y + x*y + x + y > n) break@y
            z@for (z in 1..n) {
                val tmp = x*x + y*y + z*z + x*y + y*z + z*x
                if (tmp <= n) {
                    ans[tmp-1]++
                } else {
                    break@z
                }
            }
        }
    }

    println(ans.joinToString(separator = System.lineSeparator()))
}