You are given a tree with $$$n$$$ vertices, labeled from $$$1$$$ to $$$n$$$. Each vertex $$$i$$$ has a hidden label $$$v_i$$$, and the array of hidden values $$$[v_1, v_2, \ldots, v_n]$$$ forms a permutation of integers from $$$1$$$ to $$$n$$$.
You are not given the hidden values directly. Instead, you are given the structure of the tree and the weights of its $$$n - 1$$$ edges. The weight of the edge connecting vertex $$$i$$$ and vertex $$$j$$$ is $$$v_i \oplus v_j$$$, where $$$\oplus$$$ denotes the bitwise XOR operation.
Your task is to reconstruct the hidden labels $$$v_1, v_2, \dots v_n$$$ with the given information.
The first line contains a single integer $$$t$$$ $$$(1 \leq t \leq 100)$$$, representing the number of test cases.
The first line of each test case contains $$$n$$$ $$$(1 \leq n \leq 2 \cdot 10^5)$$$, the number of vertices in the tree.
The next $$$n - 1$$$ lines of each test case each contain three integers $$$i$$$, $$$j$$$, and $$$v_i \oplus v_j$$$ and each represent an edge in the tree.
It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$5 \cdot 10^5$$$.
On a single line, output the labels of vertices $$$1, 2, 3, \ldots, n$$$ in order.
If there are multiple solutions, you can output any of them.
| Subtask | Constraint | Points |
| $$$1$$$ | $$$n$$$ is odd | $$$30$$$ |
| $$$2$$$ | $$$\sum n \leq 5000$$$ | $$$30$$$ |
| $$$3$$$ | No additional constraints | $$$90$$$ |
1 5 1 2 7 1 3 5 3 4 4 3 5 3
4 3 1 5 2
The labels satisfy the constraints because we have
