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 Julia (0.5.0) (judge verdict: Accepted)

parseInt(x) = parse(Int,x)
function division(x)
	y = Int[]
	i = 2
	while x > 1 || i <= sqrt(x)
		if x%i == 0
			push!(y, i)
			x = div(x, i)
		else
			i += 1
		end
	end
	return(y)
end

function main()
	n = parseInt(readline())
	x = Int[]
	for i in 1:n
		append!(x,division(i))
	end
	d = Dict{Int,Int}()
	for i in 1:length(x)
		if haskey(d,x[i])
			d[x[i]] += 1
		else
			d[x[i]] = 1
		end
	end
	two = 0
	four = 0
	ft = 0
	tf = 0
	sf = 0
	for i in values(d)
		if i >= 74
			sf += 1
		end
		if i >= 24
			tf += 1
		end
		if i >= 14
			ft += 1
		end
		if i >= 4
			four += 1
		end
		if i >= 2
			two += 1
		end
	end
	a0 = max(tf * (two-1),0)
	a1 = max(ft * (four-1),0)
	a2 = max(div((four)*(four-1),2)*(two-2),0)
	print(a0+a1+a2+sf)
end
main()