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)

private fun readLn() = readLine()!!
private fun readInt() = readLn().toInt()
private fun readLong() = readLn().toLong()
private fun readStrings() = readLn().split(" ")
private fun readInts() = readStrings().map(String::toInt)
private fun readLongs() = readStrings().map(String::toLong)

fun main() {
    val m = 10000
    val cnt = IntArray(m + 1)
    for (x in 1..100)
        for (y in 1..100)
            for (z in 1..100) {
                val res = x * x + y * y + z * z + x * y + y * z + x * z
                if (res > m) continue
                cnt[res]++
            }
    val n = readInt()
    println(cnt.take(n + 1).takeLast(n).joinToString("\n"))
}