Given an undirected, weighted graph of n vertices and m edges. Find the shortest path from 1 to n.
### Input
- The first line contains 2 integers n,m.
- The next m lines, each line contains 3 integers u,v,w, there is an edge of weight w connecting u,v .
### Output
- Print the weight of the shortest path on one line, then print the path on another line. Print -1 if no solution exists. In case there are more than 1 solution, print any.
### Constraints
- 1≤n,m≤2×105.
- 1≤u,v≤n.
- 1≤w≤109.
### Example
Input:
33121232133
Output:
3123