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'

n = gets.strip.to_i

divided = n.downto(1).inject({}) {|memo, num|
  num.prime_division.each {|div, count|
    if memo[div].nil?
      memo[div]=count
    else
      memo[div]+=count 
    end
  }
  memo
}.to_a

factor_counts = divided.map(&:last)

counts_4_arr = factor_counts.select {|f| f >= 4 }.to_a
counts_4 = factor_counts.select {|f| f >= 4 }.to_a.length
counts_2 = factor_counts.select {|f| f >= 2 }.to_a.length
counts_14 = factor_counts.select {|f| f >= 14 }.to_a.length
counts_24 = factor_counts.select {|f| f >= 24 }.to_a.length
counts_74 = factor_counts.select {|f| f >= 74 }.to_a.length

with_4_4_2 =  counts_4_arr.combination(2).to_a.length * (counts_2-2)
with_24_2 =  counts_24 * (counts_2-1)
with_14_4 = counts_14 * (counts_4-1)
with_74_0 = counts_74

p with_4_4_2 + with_24_2 + with_14_4 + with_74_0