#abc185c. [abc185_c]Duodecim Ferra
[abc185_c]Duodecim Ferra
Problem Statement
There is an iron bar of length lying east-west. We will cut this bar at positions to divide it into bars. Here, each of the resulting bars must have a positive integer length.
Find the number of ways to do this division. Two ways to do the division are considered different if and only if there is a position cut in only one of those ways.
Under the constraints of this problem, it can be proved that the answer is less than .
Constraints
- is an integer.
Input
Input is given from Standard Input in the following format:
Output
Print the number of ways to do the division.
Sample Input 1
12
Sample Output 1
1
There is only one way: to cut the bar into bars of length each.
Sample Input 2
13
Sample Output 2
12
Just one of the resulting bars will be of length . We have options: one where the westmost bar is of length , one where the second bar from the west is of length , and so on.
Sample Input 3
17
Sample Output 3
4368