Problem B: Find the depth

## Problem B: Find the depth

Time Limit: 1 Sec  Memory Limit: 128 MB
Submit: 717  Solved: 221
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## Description

Given a tree with N nodes and N-1 edges, the length of each edge is 1, the root of the tree is node 1, please find the depth of all nodes. the depth for node 1 is 0.

## Input

The first line will be a integer T $$(1 \leq T \leq 10)$$, which is the number of test cases.
For each test data:
The first line contains an integer N $$(1 \leq N \leq 10^5 )$$ — the number of nodes.
the next N-1 lines contain two integers a and b $$(1 \leq a,b \leq N)$$, which means there is an edge between node a and b.

## Output

For each case, print one line with N integers, the i-th integer indicates the depth of node i.

## Sample Input

1
4
1 2
1 3
4 2

## Sample Output

0 1 1 2

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