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 $i^{th}$ edge belongs to at least one minimum spanning tree, the $i^{th}$ character should be `1`, otherwise `0`.
### Constraints
- $1 \le n, m \le 10^5$.
- $1 \le u, v \le n$.
- $1 \le w \le 10^9$
### Example
Input:
```
4 7
1 2 2
2 3 2
4 1 1
3 2 5
1 4 4
1 2 1
4 2 3
```
Output:
```
0110010
```
