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 Go (1.6) (judge verdict: Accepted)

// Package main provides
//
// File:  d.go
// Author: ymiyamoto
//
// Created on Mon Dec 17 15:23:05 2018
//
package main

import "fmt"

func nums(slice []int, f func(n int) bool) int {
	count := 0
	for _, s := range slice {
		if f(s) {
			count++
		}
	}
	return count
}

func gTE(n int) func(n int) bool {
	return func(m int) bool { return m >= n-1 }
}

func main() {
	var N int
	fmt.Scan(&N)

	m := map[int]int{}
	for i := 2; i <= N; i++ {
		n := i
		for j := 2; j <= i; j++ {
			for n%j == 0 {
				m[j]++
				n /= j
			}
		}
	}

	arr := make([]int, 0)
	for _, v := range m {
		arr = append(arr, v)
	}

	ans := nums(arr, gTE(75)) + nums(arr, gTE(25))*(nums(arr, gTE(3))-1) + nums(arr, gTE(15))*(nums(arr, gTE(5))-1) + nums(arr, gTE(5))*(nums(arr, gTE(5))-1)*(nums(arr, gTE(3))-2)/2
	fmt.Println(ans)
}