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

dim=Array.new(n+1, 0)
(1..n).each do |c|
  c.prime_division.each do |b, d|
    dim[b]+=d
  end
end

result=0
target_pairs = [[5,5,3], [15, 5], [25,3], [75]]

targets = dim.select {|e| e>0 }
targets.length.times do |i|
end

targets.combination(3).each do |a, b, c|
  result+=1 if (a>=4 && b>= 4 && c >= 2)
  result+=1 if (a>=4 && b>= 2 && c >= 4)
  result+=1 if (a>=2 && b>= 4 && c >= 4)
end

targets.combination(2).each do |a, b|
  [ [14, 4], [24, 2] ].each do |t1, t2|
    result+=1 if (a>=t1 && b>= t2)
    result+=1 if (a>=t2 && b>=t1)
  end
end

result+=targets.select {|e| e>=74 }.length

p result
#p targets