Southern California Regional of the ACM International Collegiate Programming Contest


PREVIOUS CONTEST PROBLEM


Factorial Factors

The factorial function, n! = 1 2 ... n, has many interesting properties. In this problem, we want to determine the maximum number of integer terms (excluding 1) that can be used to express n!. For example:

8! = 1 2 3 4 5 6 7 8 = 2 3 2 2 5 3 2 7 2 2 2 = 27 32 5 7

By inspection, it is clear that the maximum number of terms (excluding 1) that can be multiplied together to produce 8! is 11.

The input for your program consists of a series of test cases on separate lines, ended by end-of-file. Each line contains one number, n, 2 <= n <= 1000000.

For each test case, print the maximum number of factors (excluding 1) that can be multiplied together to produce n!. Put the output from each test case on a separate line, starting in the first column.

 

Sample Input

2
1000000
1996
5
8
123456

 

Sample Output

 

1
3626619
5957
5
11
426566