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: Time Limit Exceeded)

fun main() {
    var n = readLine()!!.toInt()

    println(0)
    for(k in 2..n) {
        var c = 0
        for(i in 1..k) {
            if(i * i > k) continue
            for (j in 1..k) {
                if(j * j > k) continue
                if(i * j > k) continue

                var l = 1
                var r = k / 2 + 1
                var m = r / 2
                while (l <= r) {
                    var a = i * i + j * j + i * j + m * m + i * m + j * m
                    var b = k
//                    println("$i $j $m $a $l $r")
                    if (m == 0) continue
                    if (a == b) {
                        c++
                        break
                    } else if (a > b) {
                        r = m - 1
                    } else {
                        l = m + 1
                    }
                    m = (l + r) / 2
                }
            }
        }
        println(c)
    }
}