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'
io = STDIN
N=io.gets.to_i

PD= (1..N).inject(:*).prime_division.select{|k,v|v>=2}.to_h
def gt_cnt(n)
  PD.values.count{|i|i>=n.pred}
end
#75
#3*25
#3*5*5
#5*15
cnt=0
ar= [[75],[25,3],[5,5,3],[15,5]].map do |nums|
  dup=nums.size-nums.uniq.size
  nums.map.with_index do |n,i|
    (gt_cnt(n)-i)
  end.inject(:*)/(dup+1)
end
puts ar.inject(:+)