Tree Edges XOR

AtCoder

IDagc052_b

Time2000ms

Memory256MB

Difficulty—

You are given a tree with $N$ vertices, where $N$ is **odd**. The vertices are numbered from $1$ through $N$ and edges from $1$ through $N-1$. The edge $i$ connects vertices $u_i$ and $v_i$ and its initial weight is $w^1_i$. You can perform the following operation any number of times: * Choose an edge $(u, v)$ of the tree, and suppose that its weight now is $w$. For every edge, which is incident to exactly one of $u$ and $v$, we **XOR** the weight of that edge with $w$ (if it was $w_1$, replace it with $w_1 \oplus w$). Your goal is to reach the state where each edge $i$ has weight $w^2_i$. Determine if you can get to the goal by performing the operation above any number of times. ## Constraints * $1 \le N \le 10^5$ * $N$ is odd. * $1\le u_i, v_i \le N$ * $u_i \neq v_i$ * $0\le w^1_i, w^2_i < 2^{30}$ * All values in input are integers. * The input represents a valid tree. ## Input Input is given from Standard Input in the following format: $N$ $u_1$ $v_1$ $w^1_1$ $w^2_1$ $u_2$ $v_2$ $w^1_2$ $w^2_2$ $\vdots$ $u_{N-1}$ $v_{N-1}$ $w^1_{N-1}$ $w^2_{N-1}$ [samples]

Samples

Input #1

3
1 2 1 1
2 3 8 9

Output #1

YES

If you perform the operation on the edge $1$, the weight of the edge $2$ becomes $8 \oplus 1=9$.

Input #2

Output #2

NO

API Response (JSON)

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    "name": "Tree Edges XOR",
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      "content": "You are given a tree with $N$ vertices, where $N$ is **odd**. The vertices are numbered from $1$ through $N$ and edges from $1$ through $N-1$. The edge $i$ connects vertices $u_i$ and $v_i$ and its in",
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      "statement_type": "Markdown",
      "content": "You are given a tree with $N$ vertices, where $N$ is **odd**. The vertices are numbered from $1$ through $N$ and edges from $1$ through $N-1$. The edge $i$ connects vertices $u_i$ and $v_i$ and its in...",
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