Given a tree of n vertices. Count the number of simple paths with length k.
### Input
- The first line contains an integer n.
- The next n−1 lines, each line contains 2 integers u,v, there is an edge between u and v.
### Output
- Print the number of paths with length k.
### Constraints
- 1≤n≤105.
- 1≤k≤100.
- 1≤u,v≤n.
### Example
Input:
5212231445
Output:
3