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)

N = readline.chomp.to_i

require 'prime'

merged = {}
(1..N).to_a.each do |n|
  ps = Hash[Prime.prime_division(n)]
  ps.each {|k,v| merged[k] = (merged[k] || 0) + v }
end

exps = merged.values.sort

# count 75
c1 = exps.count {|x| x >= 74}

# count 25 x 3
n25 = exps.count {|x| x >= 24}
n3 = exps.count {|x| x >= 2}
c2 = n25 * (n3-1)

# count 15 x 5
n15 = exps.count {|x| x >= 14}
n5 = exps.count {|x| x >= 4}
c3 = n15 * (n5-1)

# count 5 x 5 x 3
n5 = exps.count {|x| x >= 4}
n3 = exps.count {|x| x >= 2}
c4 = n5*(n5-1)/2 * (n3-2)

puts c1+c2+c3+c4