No testdata at current.

Description

Input

The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

The first line of each test case contains a single integer $n$ ($2 \le n \le 3 \cdot 10^5$).

Each of the next $n−1$ lines contains two integers $u$ and $v$ ($1 \le u,v \le n$) indicating that there is an edge between vertices $u$ and $v$. It is guaranteed that the given edges form a tree.

It is guaranteed that the sum of $n$ over all test cases doesn't exceed $3 \cdot 10^5$.

Output

For each test case, print $n$ integers in a single line, $x$-th of which is equal to $f(x)$ for all $x$ from $1$ to $n$.

3
4
1 2
2 3
1 4
2
1 2
7
1 2
1 3
3 4
3 5
3 6
5 7
 
 
 
 
 
 
 
 
 
 
 

1 2 2 2 
1 1 
2 2 3 3 3 3 3

Note

• For $x = 1$, we can an edge between vertices $1$ and $3$, then $d(1) = 0$ and $d(2) = d(3) = d(4) = 1$, so $f(1) = 1$.
• For $x \ge 2$, no matter which edge we add, $d(1) = 0$, $d(2) = d(4) = 1$ and $d(3) = 2$, so $f(x) = 2$.