You are given a weighted tree with $$$n$$$ vertices. Recall that a tree is a connected graph without any cycles. A weighted tree is a tree in which each edge has a certain weight. The tree is undirected, it doesn't have a root.

Since trees bore you, you decided to challenge yourself and play a game on the given tree.

In a move, you can travel from a node to one of its neighbors (another node it has a direct edge with).

You start with a variable $$$x$$$ which is initially equal to $$$0$$$. When you pass through edge $$$i$$$, $$$x$$$ changes its value to $$$x ~\mathsf{XOR}~ w_i$$$ (where $$$w_i$$$ is the weight of the $$$i$$$-th edge).

Your task is to go from vertex $$$a$$$ to vertex $$$b$$$, but you are allowed to enter node $$$b$$$ if and only if after traveling to it, the value of $$$x$$$ will become $$$0$$$. In other words, you can travel to node $$$b$$$ only by using an edge $$$i$$$ such that $$$x ~\mathsf{XOR}~ w_i = 0$$$. Once you enter node $$$b$$$ the game ends and you win.

Additionally, you can teleport at most once at any point in time to any vertex except vertex $$$b$$$. You can teleport from any vertex, even from $$$a$$$.

Answer with "YES" if you can reach vertex $$$b$$$ from $$$a$$$, and "NO" otherwise.

Note that $$$\mathsf{XOR}$$$ represents the bitwise XOR operation.

Input

The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 1000$$$) — the number of test cases.

The first line of each test case contains three integers $$$n$$$, $$$a$$$, and $$$b$$$ ($$$2 \leq n \leq 10^5$$$), ($$$1 \leq a, b \leq n; a \ne b$$$) — the number of vertices, and the starting and desired ending node respectively.

Each of the next $$$n-1$$$ lines denotes an edge of the tree. Edge $$$i$$$ is denoted by three integers $$$u_i$$$, $$$v_i$$$ and $$$w_i$$$ — the labels of vertices it connects ($$$1 \leq u_i, v_i \leq n; u_i \ne v_i; 1 \leq w_i \leq 10^9$$$) and the weight of the respective edge.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^5$$$.

Output

For each test case output "YES" if you can reach vertex $$$b$$$, and "NO" otherwise.

Note

For the first test case, we can travel from node $$$1$$$ to node $$$3$$$, $$$x$$$ changing from $$$0$$$ to $$$1$$$, then we travel from node $$$3$$$ to node $$$2$$$, $$$x$$$ becoming equal to $$$3$$$. Now, we can teleport to node $$$3$$$ and travel from node $$$3$$$ to node $$$4$$$, reaching node $$$b$$$, since $$$x$$$ became equal to $$$0$$$ in the end, so we should answer "YES".

For the second test case, we have no moves, since we can't teleport to node $$$b$$$ and the only move we have is to travel to node $$$2$$$ which is impossible since $$$x$$$ wouldn't be equal to $$$0$$$ when reaching it, so we should answer "NO".

Idx	Name	Rating
A	Medium Number	800
B	Atilla's Favorite Problem	800
C	Advantage	800
D	Challenging Valleys	1000
E	Binary Inversions	1100
F	Quests	1500
G	SlavicG's Favorite Problem	1700

Codeforces Round 835 (Div. 4)