C. Ehab and Path-etic MEXstime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given a tree consisting of n nodes. You want to write some labels on the tree's edges such that the following conditions hold:  Every label is an integer between 0 and n-2 inclusive.  All the written labels are distinct.  The largest value among MEX(u,v) over all pairs of nodes (u,v) is as small as possible. Here, MEX(u,v) denotes the smallest non-negative integer that isn't written on any edge on the unique simple path from node u to node v.InputThe first line contains the integer n (2 \le n \le 10^5) — the number of nodes in the tree.Each of the next n-1 lines contains two space-separated integers u and v (1 \le u,v \le n) that mean there's an edge between nodes u and v. It's guaranteed that the given graph is a tree.OutputOutput n-1 integers. The i^{th} of them will be the number written on the i^{th} edge (in the input order).ExamplesInput
3
1 2
1 3
Output
0
1
Input
6
1 2
1 3
2 4
2 5
5 6
Output
0
3
2
4
1NoteThe tree from the second sample:
3
1 2
1 3

0 1 
['constructive algorithms', 'dfs and similar', 'greedy', 'trees', '*1500']