Given an undirected connected graph with n vertices and m edges, find the second shortest path from 1 to n. The length of this path must be greater than the shortest path.
### Input
- The first line contains two integers n and m.
- The next m lines each contain three integers u, v, and w, indicating a path of length w between u and v.
### Output
- Print an integer representing the length of the second shortest path.
### Constraints
- 1≤n,m≤105.
- 1≤u,v≤n.
- 1≤w≤104.
### Example
Input:
4412100242002325034100
Output:
450