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