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())

pn=[2];A=100
for L in range(3,A):
  chk=True
  for L2 in pn:
    if L%L2 == 0:chk=False
  if chk==True:pn.append(L)

mul = [0 for i in range(101)]
for i in range(1,N+1):
  for j in pn:
    if j > i:
      break
    temp = i
    while True:
      if temp%j == 0:
        temp /= j
        mul[j] += 1
        continue
      else:
        break
        
prime_num = []
for index, num in enumerate(mul):
  if num != 0:
    prime_num.append([index,num])

ans = 0
# 4,4,2の取り出し
from itertools import combinations
nums442 = list(combinations(prime_num,3))
for num in nums442:
  if num[0][1]>=2 and num[1][1]>=4 and num[2][1]>=4:
    ans += 1
  if num[0][1]>=4 and num[1][1]>=2 and num[2][1]>=4:
    ans += 1
  if num[0][1]>=4 and num[1][1]>=4 and num[2][1]>=2:
    ans += 1

# 14,4の取り出し
nums14_4 = list(combinations(prime_num,2))
for num in nums14_4:
  if num[0][1]>=14 and num[1][1]>=4:
    ans += 1
  if num[0][1]>=4 and num[1][1]>=14:
    ans += 1

# 24,2の取り出し
nums24_2 = list(combinations(prime_num,2))
for num in nums24_2:
  if num[0][1]>=24 and num[1][1]>=2:
    ans += 1
  if num[0][1]>=2 and num[1][1]>=24:
    ans += 1
    
# 74の取り出し
for num in prime_num:
  if num[1] >= 74:
    ans += 1
    
print(ans)