Given a connected, weighted, undirected graph of n vertices and m edges.
For every edge, determine if it belongs to at least one minimum spanning tree.
### Input
- The first line contain 2 integers n,m.
- The next m lines, each line contains 3 integers u,v,w, there is an edge weigh w between u and v.
### Output
- Print a binary string of length m. If ith edge belongs to at least one minimum spanning tree, the ith character should be 1, otherwise 0.
### Constraints
- 1≤n,m≤105.
- 1≤u,v≤n.
- 1≤w≤109
### Example
Input:
47122232411325144121423
Output:
0110010