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 PyPy3 (7.3.0) (judge verdict: Accepted)

import math
n=int(input())
p=[0]*101
dp=[0]*101
for i in range(2,n+1):
  for j in range(2,i+1):
    while i%j==0:
      i//=j
      p[j]+=1
for i in range(101):
  if p[i]!=0:
    dp[p[i]]+=1
ans=sum(dp[74:])+sum(dp[24:])*(sum(dp[2:])-1)+sum(dp[14:])*(sum(dp[4:])-1)+sum(dp[4:])*(sum(dp[4:])-1)//2*(sum(dp[2:])-2)
print(ans)