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)
	ret := solve(n)
	fmt.Println(ret)
}

func solve(n int) int {
	factors := make([]int, n+1)

	for i := 2; i <= n; i++ {
		curr := i
		for j := 2; j <= i; j++ {
			for curr%j == 0 {
				factors[j] += 1
				curr /= j
			}
		}
	}

	count := 0

	for i := 2; i <= n; i++ {
		for j := i + 1; j <= n; j++ {
			for k := j + 1; k <= n; k++ {
				if factors[i] >= 4 && factors[j] >= 4 && factors[k] >= 2 {
					count += 1
				}
				if factors[i] >= 4 && factors[j] >= 2 && factors[k] >= 4 {
					count += 1
				}
				if factors[i] >= 2 && factors[j] >= 4 && factors[k] >= 4 {
					count += 1
				}
			}
		}
	}
	for i := 2; i <= n; i++ {
		for j := i + 1; j <= n; j++ {
			if factors[i] >= 24 && factors[j] >= 2 {
				count += 1
			}
			if factors[i] >= 2 && factors[j] >= 24 {
				count += 1
			}
			if factors[i] >= 14 && factors[j] >= 4 {
				count += 1
			}
			if factors[i] >= 4 && factors[j] >= 14 {
				count += 1
			}
		}
	}
	for i := 2; i <= n; i++ {
		if factors[i] >= 74 {
			count += 1
		}
	}

	return count
}