9679: ABC185 —— C - Duodecim Ferra
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Description
There is an iron bar of length $L$ lying east-west. We will cut this bar at $11$ positions to divide it into $12$ bars. Here, each of the $12$ 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 $2^{63}$.
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 $2^{63}$.
Input
Input is given from Standard Input in the following format:
```
$L$
```
```
$L$
```
Output
Print the number of ways to do the division.
Constraints
- $12 \le L \le 200$
- $L$ is an integer.
- $L$ is an integer.
Sample 1 Input
12
Sample 1 Output
1
There is only one way: to cut the bar into 12 bars of length 1 each.
Sample 2 Input
13
Sample 2 Output
12
Just one of the resulting bars will be of length 2. We have 12 options: one where the westmost bar is of length 2, one where the second bar from the west is of length 2, and so on.
Sample 3 Input
17
Sample 3 Output
4368