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

import "fmt"

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

	p := make([]int, 0, 0)

	for i := 2; i <= n; i++ {
		tmp := true
		for j := 2; j * j <= i; j++ {
			if i % j == 0 {
				tmp = false
				break
			}
		}
		if tmp {
			p = append(p, i)
		}
	}

	l := len(p)
	a := make([]int, l, l)

	for i := 0; i < l; i++ {
		c := 0
		for d := p[i]; d < n; d *= p[i] {
			c += n / d
		}
		a[i] = c
	}

	answer := 0

	for i := 0; i < l; i++ {
		if a[i] >= 75 - 1 {
			answer++
		}
	}

	for i := 0; i < l; i++ {
		for j := 0; j < l; j++ {
			if (i == j) {
				continue
			}
			if a[i] >= 3 - 1 && a[j] >= 25 - 1 {
				answer++
			}
		}
	}

	for i := 0; i < l; i++ {
		for j := 0; j < l; j++ {
			if (i == j) {
				continue
			}
			if a[i] >= 5 - 1 && a[j] >= 15 - 1 {
				answer++
			}
		}
	}

	for i := 0; i < l; i++ {
		for j := 0; j < l; j++ {
			for k := j + 1; k < l; k++ {
				if (i == j || i == k) {
					continue
				}
				if a[i] >= 3 - 1 && a[j] >= 5 - 1 && a[k] >= 5 - 1 {
					answer++
				}	
			}
		}
	}

	fmt.Println(answer)
}