13011301 SUSTech Online Judge
Problem 1301 --Distance in the country

## 1301: Distance in the country

Time Limit: 1 Sec  Memory Limit: 128 MB
Submit: 55  Solved: 29
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## Description

There are $$n$$ cities in the country with $$n-1$$ roads connecting them. In other words, the country can be represented as a tree. Pisces is now in city $$1$$, and he wants to know the distance from his current position to each of the other cities. Here the distance between cities $$A$$ and $$B$$ is defined as the number of roads in the simple path (a path without duplicate cities) from $$A$$ to $$B$$.

## Input

The first line contains an interger $$T(1\leq T\leq 10)$$, which represents the number of test cases.

For each of the test case, the first line contains an integer $$n(1\leq n\leq 10^4)$$, which is the number of cities. Each of the next $$n-1$$ lines contains $$2$$ interger $$u$$ and $$v(1\leq u, v\leq n)$$, representing that there is a road from city $$u$$ to city $$v$$.

## Output

For each test case, print $$n$$ integers. The $$i$$-th interger represents the distance from city $$1$$ to city $$i$$. Especially, the distance of city $$1$$ itself is $$0$$.

## Sample Input

1
5
1 2
1 3
2 4
4 5

## Sample Output

0 1 1 2 3

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