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)

input = STDIN.readlines.map{|line|line.strip.split()}
line = input.shift
n = line[0].to_i

counts = Hash.new(0)
Range.new(2, n).each do |out_r|
    temp = out_r
    while temp > 1
        Range.new(2, temp).each do |in_r|
            if temp % in_r == 0 then
                counts[in_r] += 1
                temp /= in_r
                break
            end
        end
    end
end
ans = 0
ans += counts.select{|k,c|c>=74}.size
ans += counts.select{|k,c|c>=24}.size * (counts.select{|k,c|c>=2}.size - 1)
ans += counts.select{|k,c|c>=14}.size * (counts.select{|k,c|c>=4}.size - 1)
if counts.select{|k,c|c>=4}.size >= 2 then
    ans += counts.select{|k,c|c>=4}.size * (counts.select{|k,c|c>=4}.size - 1) / 2 * (counts.select{|k,c|c>=2}.size - 2)
end
puts(ans)