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 (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var sc, wr = bufio.NewScanner(os.Stdin), bufio.NewWriter(os.Stdout)

func scanString() string { sc.Scan(); return sc.Text() }
func scanRunes() []rune { return []rune(scanString()) }
func scanInt() int { a,_ := strconv.Atoi(scanString()); return a }
func scanInt64() int64 { a,_ := strconv.ParseInt(scanString(),10,64); return a }
func scanFloat64() float64 { a,_ := strconv.ParseFloat(scanString(),64); return a }

func scanInts(n int) []int {
	res := make([]int, n); for i := 0; i < n; i++ { res[i] = scanInt() }; return res
}

func debug(a ...interface{}) { fmt.Fprintln(os.Stderr, a...) }

func abs(a int) int { if a<0 { return -a }; return a }
func min(a,b int) int { if a<b { return a }; return b }
func max(a,b int) int { if a>b { return a }; return b }

//•*¨*•.¸¸♪Main•*¨*•.¸¸♪(　-ω-)ノ　(　・ω・)

func main() {
	defer wr.Flush()
	sc.Split(bufio.ScanWords)
	sc.Buffer(make([]byte, 10000), 1001001)

	n := scanInt()

	cnt := map[int]int{}

	factorize := func(n int) {
		for i := 2; i*i <= n; i++ {
			for n%i == 0 {
				cnt[i]++
				n /= i
			}
		}

		if n!= 1 {
			cnt[n]++
		}
	}

	for i := 2; i <= n; i++ {
		factorize(i)
	}

	dp := make([][76]int, len(cnt)+1)
	dp[0][1] = 1
	// debug(dp[0])

	c := 0
	for _, e := range cnt {
		for i := 1; i < 76; i++ {
			for j := 1; j < e+2; j++ {
				if i*j > 75 {
					continue
				}
				dp[c+1][i*j] += dp[c][i]
			}
		}
		// debug(e,dp[c+1])
		c++
	}

	fmt.Fprintln(wr, dp[len(cnt)][75])
}