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 = 2^{7 .} 3^{2 .} 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.

Input 

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$\le$n$\le$1000000.

Output 

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