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 Ruby (2.3.3) (judge verdict: Accepted)

require 'prime'

def factorial(number)
  (1..number).inject(1,:*)
end

n = gets.chomp.to_i

s = factorial(n).prime_division.map{|a| a[1]}

total = 0

# 75
count75 = s.select{|x| x >= 74}.size

total += count75

# 25, 3
count25 = s.select{|x| x >= 24}.size
count3 = s.select{|x| x >= 2}.size

total += count25 * (count3 - 1)

# 15, 5
count15 = s.select{|x| x >= 14}.size
count5 = s.select{|x| x >= 4}.size

total += count15 * (count5 - 1)

# 5, 5, 3
total += count5 * (count5 - 1) * (count3 - 2) / 2

puts total