Problem:
Score : 400 points

Problem Statement

You are given an integer N. Among the divisors of N! (= 1 \times 2 \times ... \times N), how many Shichi-Go numbers (literally "Seven-Five numbers") are there?

Here, a Shichi-Go number is a positive integer that has exactly 75 divisors.

Note

When a positive integer A divides a positive integer B, A is said to a divisor of B.
For example, 6 has four divisors: 1, 2, 3 and 6.

Constraints

1 \leq N \leq 100

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

Print the number of the Shichi-Go numbers that are divisors of N!.

Sample Input 1

9

Sample Output 1

0

There are no Shichi-Go numbers among the divisors of 9! = 1 \times 2 \times ... \times 9 = 362880.

Sample Input 2

10

Sample Output 2

1

There is one Shichi-Go number among the divisors of 10! = 3628800: 32400.

Sample Input 3

100

Sample Output 3

543

Solution in Scala (2.11.7) (judge verdict: Accepted)

object Main {
  def main(args: Array[String]): Unit = {
    val s = new Main()
    s.solve()
    s.out.flush()
  }
}

class Main {
  import java.io._
  import java.util.StringTokenizer

  import scala.collection.mutable
  import scala.util.Sorting
  import math.{abs, max, min}
  import mutable.{ArrayBuffer, ListBuffer}
  import scala.reflect.ClassTag

  val MOD = 1000000007
  val out = new PrintWriter(System.out)

  def solve(): Unit = {
    val N = ni()

    def add(a: mutable.Map[Int, Int], b: mutable.Map[Int, Int]): mutable.Map[Int, Int] = {
      val res = mutable.Map[Int, Int]().withDefaultValue(0)
      res ++= a
      b.foreach { case (f, cnt) => res(f) = res(f) + cnt }
      res
    }

    val factors = map(N - 1, 2) { i =>
      factorize(i)
    }.foldLeft(mutable.Map[Int, Int]())(add)

    val C = factors.values.toArray
    var ans = 0

    def count1(a: Int) = {
      C.count(_ >= a - 1)
    }

    // a < b
    def count2(a: Int, b: Int) = {
      val cb = C.count(_ >= b - 1)
      val ca = C.count(_ >= a - 1) - cb

      ca * cb + (if (cb > 1) cb * (cb - 1) else 0)
    }

    // a < b == c
    def count3(a: Int, b: Int) = {
      val cb = C.count(_ >= b - 1)
      val ca = C.count(_ >= a - 1) - cb

      var res = 0
      if (cb > 1) {
        res += ca * cb * (cb - 1) / 2
      }
      if (cb > 2) {
        res += cb * (cb - 1) * (cb - 2) / 2
      }
      res
    }

    ans += count1(75)
    ans += count2(5, 15)
    ans += count2(3, 25)
    ans += count3(3, 5)


    out.println(ans)
  }

  /**
    * *注意* IntをLongにして使わないこと
    */
  def factorize(n: Int): mutable.Map[Int, Int] = {
    import scala.collection.mutable
    val res = mutable.Map[Int, Int]() withDefaultValue 0

    def minFactor(n0: Int, rt: Int, i: Int): Int = {
      if (i > rt) n0 // √n まで見つからなかったら n0は素数か1
      else if (n0 % i == 0) i
      else minFactor(n0, rt, i + 1)
    }

    def step(n0: Int): Unit = {
      minFactor(n0, math.sqrt(n0).toInt, 2) match {
        case 1 =>
        case f =>
          res(f) = res(f) + 1
          step(n0 / f)
      }
    }

    step(n)
    res
  }

  class InputReader(val stream: InputStream) {
    private val reader = new BufferedReader(new InputStreamReader(stream), 32768)
    private var tokenizer: StringTokenizer = _

    def next(): String = {
      while (tokenizer == null || !tokenizer.hasMoreTokens)
        tokenizer = new StringTokenizer(reader.readLine)
      tokenizer.nextToken
    }

    def nextInt(): Int = next().toInt
    def nextLong(): Long = next().toLong
    def nextChar(): Char = next().charAt(0)
  }
  val sc = new InputReader(System.in)
  def ni(): Int = sc.nextInt()
  def nl(): Long = sc.nextLong()
  def nc(): Char = sc.nextChar()
  def ns(): String = sc.next()
  def ns(n: Int): Array[Char] = ns().toCharArray
  def na(n: Int, offset: Int = 0): Array[Int] = map(n)(_ => ni() + offset)
  def na2(n: Int, offset: Int = 0): (Array[Int], Array[Int]) = {
    val A1, A2 = Array.ofDim[Int](n)
    REP(n) { i =>
      A1(i) = ni() + offset
      A2(i) = ni() + offset
    }
    (A1, A2)
  }
  def nm(n: Int, m: Int): Array[Array[Int]] = {
    val A = Array.ofDim[Int](n, m)
    REP(n) { i =>
      REP(m) { j =>
        A(i)(j) = ni()
      }
    }
    A
  }
  def nal(n: Int): Array[Long] = map(n)(_ => nl())
  def nm_c(n: Int, m: Int): Array[Array[Char]] = map(n) (_ => ns(m))
  def REP(n: Int, offset: Int = 0)(f: Int => Unit): Unit = {
    var i = offset
    val N = n + offset
    while(i < N) { f(i); i += 1 }
  }
  def REP_r(n: Int, offset: Int = 0)(f: Int => Unit): Unit = {
    var i = n - 1 + offset
    while(i >= offset) { f(i); i -= 1 }
  }

  def map[@specialized A: ClassTag](n: Int, offset: Int = 0)(f: Int => A): Array[A] = {
    val res = Array.ofDim[A](n)
    REP(n)(i => res(i) = f(i + offset))
    res
  }


  def sumL(as: Array[Int]): Long = {
    var s = 0L
    REP(as.length)(i => s += as(i))
    s
  }

  def cumSum(as: Array[Int]) = {
    val cum = Array.ofDim[Long](as.length + 1)
    REP(as.length) { i =>
      cum(i + 1) = cum(i) + as(i)
    }
    cum
  }
}