Codeforces Round 628 (Div. 2) |
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Finished |

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constructive algorithms

dfs and similar

greedy

trees

*1500

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C. Ehab and Path-etic MEXs

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard 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 $$$v$$$.

Input

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.

Output

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

Examples

Input

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 1

Note

The tree from the second sample:

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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