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)

import java.io.BufferedReader
import java.io.InputStream
import java.io.InputStreamReader
import java.util.*
import kotlin.math.abs
import kotlin.math.max
import kotlin.math.min

val MOD = 1_000_000_007L

class Solver(stream: InputStream, private val out: java.io.PrintWriter) {
  fun solve() {
    val N = ni()
    val dp = LongArray(N + 1)
    for (x in 1 .. 100) {
      for (y in 1 .. 100) {
        for (z in 1 .. 100) {
          val n = x * x + y * y + z * z + x * y + x * z + y * z
          if (n in 1 .. N) dp[n]++
        }
      }
    }
    for (i in 1 .. N) {
      out.println(dp[i])
    }
  }













































  private val isDebug = try {
    // なんか本番でエラーでる
    System.getenv("MY_DEBUG") != null
  } catch (t: Throwable) {
    false
  }

  private var tokenizer: StringTokenizer? = null
  private val reader = BufferedReader(InputStreamReader(stream), 32768)
  private fun next(): String {
    while (tokenizer == null || !tokenizer!!.hasMoreTokens()) {
      tokenizer = StringTokenizer(reader.readLine())
    }
    return tokenizer!!.nextToken()
  }

  private fun ni() = next().toInt()
  private fun nl() = next().toLong()
  private fun ns() = next()
  private fun na(n: Int, offset: Int = 0): IntArray {
    return map(n) { ni() + offset }
  }
  private fun nal(n: Int, offset: Int = 0): LongArray {
    val res = LongArray(n)
    for (i in 0 until n) {
      res[i] = nl() + offset
    }
    return res
  }

  private fun na2(n: Int, offset: Int = 0): Array<IntArray> {
    val a  = Array(2){IntArray(n)}
    for (i in 0 until n) {
      for (e in a) {
        e[i] = ni() + offset
      }
    }
    return a
  }

  private inline fun map(n: Int, f: (Int) -> Int): IntArray {
    val res = IntArray(n)
    for (i in 0 until n) {
      res[i] = f(i)
    }
    return res
  }

  private inline fun debug(msg: () -> String) {
    if (isDebug) System.err.println(msg())
  }

  private fun debug(a: LongArray) {
    debug { a.joinToString(" ") }
  }

  private fun debug(a: IntArray) {
    debug { a.joinToString(" ") }
  }

  private fun debug(a: BooleanArray) {
    debug { a.map { if (it) 1 else 0 }.joinToString("") }
  }

  private fun debugDim(A: Array<LongArray>) {
    if (isDebug) {
      for (a in A) {
        debug(a)
      }
    }
  }
  private fun debugDim(A: Array<IntArray>) {
    if (isDebug) {
      for (a in A) {
        debug(a)
      }
    }
  }

  /**
   * 勝手にimport消されるのを防ぎたい
   */
  private fun hoge() {
    min(1, 2)
    max(1, 2)
    abs(-10)
  }
}

fun main() {
  val out = java.io.PrintWriter(System.out)
  Solver(System.`in`, out).solve()
  out.flush()
}