Blue and Red Tree

AtCoder

IDagc014_e

Time6000ms

Memory256MB

Difficulty—

There is a tree with $N$ vertices numbered $1$ through $N$. The $i$\-th of the $N-1$ edges connects vertices $a_i$ and $b_i$. Initially, each edge is painted blue. Takahashi will convert this blue tree into a red tree, by performing the following operation $N-1$ times: * Select a simple path that consists of only blue edges, and remove one of those edges. * Then, span a new red edge between the two endpoints of the selected path. His objective is to obtain a tree that has a red edge connecting vertices $c_i$ and $d_i$, for each $i$. Determine whether this is achievable. ## Constraints * $2 ≤ N ≤ 10^5$ * $1 ≤ a_i,b_i,c_i,d_i ≤ N$ * $a_i ≠ b_i$ * $c_i ≠ d_i$ * Both input graphs are trees. ## Input Input is given from Standard Input in the following format: $N$ $a_1$ $b_1$ : $a_{N-1}$ $b_{N-1}$ $c_1$ $d_1$ : $c_{N-1}$ $d_{N-1}$ [samples]

Samples

Input #1

Output #1

YES

The objective is achievable, as below:

*   First, select the path connecting vertices $1$ and $3$, and remove a blue edge $1-2$. Then, span a new red edge $1-3$.
*   Next, select the path connecting vertices $2$ and $3$, and remove a blue edge $2-3$. Then, span a new red edge $2-3$.

Input #2

Output #2

YES

Input #3

Output #3

NO

API Response (JSON)

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      "statement_type": "Markdown",
      "content": "There is a tree with $N$ vertices numbered $1$ through $N$. The $i$\\-th of the $N-1$ edges connects vertices $a_i$ and $b_i$.\nInitially, each edge is painted blue. Takahashi will convert this blue tre...",
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Full JSON Raw Segments