CF1325C.Ehab and Path-etic MEXs

普及/提高-

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题目描述

You 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 $v$ .

输入格式

The 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.

输出格式

Output $n-1$ integers. The $i^{th}$ of them will be the number written on the $i^{th}$ edge (in the input order).

输入输出样例

输入#1
```
3
1 2
1 3
```
输出#1
```
0
1
```
输入#2
```
6
1 2
1 3
2 4
2 5
5 6
```
输出#2
```
0
3
2
4
1
```

说明/提示

The tree from the second sample:

首页