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