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

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Southern California Regional of the ACM International Collegiate Programming Contest