Factorial Factors

                                    Time Limit : 5 Seconds   Memory Limit : 65535 Bytes


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, 0 <= 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



--------------------------------------------------------------------------------

Southern California Regional of the ACM International Collegiate Programming Contest