You are given a tree with $$$n$$$ vertices.

You need to construct an array $$$a_1, a_2, \ldots, a_n$$$ of length $$$n$$$, consisting of unique integers from $$$1$$$ to $$$2 \cdot n$$$, and such that for each edge $$$u_i \leftrightarrow v_i$$$ of the tree, the value $$$|a_{u_i} - a_{v_i}|$$$ is not a prime number.

Find any array that satisfies these conditions, or report that there is no such array.

Input format:
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$2 \le n \le 2 \cdot 10^5$$$) — the number of vertices in the tree.

The next $$$n - 1$$$ lines contain the edges of the tree, one edge per line. The $$$i$$$-th line contains two integers $$$u_i$$$ and $$$v_i$$$ ($$$1 \le u_i, v_i \le n$$$; $$$u_i \neq v_i$$$), denoting the edge between the nodes $$$u_i$$$ and $$$v_i$$$.

It's guaranteed that the given edges form a tree.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10 ^ 5$$$.
Output format:
For each test case, if an array that satisfies the conditions exists, print its elements $$$a_1, a_2, \ldots, a_n$$$. Otherwise, print $$$-1$$$.
Example Input 0:
2
5
1 2
2 3
2 4
3 5
7
1 2
1 3
2 4
3 5
3 6
3 7

Example Output 0:
2 10 1 6 5 
8 7 12 1 4 6 3

Notes:
The possible answers are shown below. Instead of the vertex numbers, the corresponding elements of the array $$$a$$$ are written in them.

The image of the tree in the first test case

The image of the tree in the second test case

Example input:
2
5
1 2
2 3
2 4
3 5
7
1 2
1 3
2 4
3 5
3 6
3 7


Example output:
2 10 1 6 5 
8 7 12 1 4 6 3