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 Python (3.4.3) (judge verdict: Accepted)

N = int(input())
M = {}
for n in range(1, N+1):
  f = 2
  while n > 1:
    if n%f == 0:
      if not(f in M): M[f] = 0
      M[f] += 1
      n = n//f
    else:
      f += 1
#print(M)
fs2 = list(filter(lambda f: M[f] >= 2, M))
fs4 = list(filter(lambda f: M[f] >= 4, M))
fs14 = list(filter(lambda f: M[f] >= 14, M))
fs24 = list(filter(lambda f: M[f] >= 24, M))
fs74 = list(filter(lambda f: M[f] >= 74, M))
#print(fs2, fs4, fs14, fs24, fs74)
ps = set()
for f in fs74:
  ps.add(f**74)
for f1 in fs24:
  for f2 in fs2:
    if len({ f1, f2 }) == 2:
      ps.add(f1**24*f2**3)
for f1 in fs14:
  for f2 in fs4:
    if len({ f1, f2 }) == 2:
      ps.add(f1**14*f2**4)
for f1 in fs4:
  for f2 in fs4:
    for f3 in fs2:
      if len({ f1, f2, f3 }) == 3:
        ps.add(f1**4*f2**4*f3**2)
#print(ps)
r = len(ps)
print(r)