Isomorphic?

You are given two undirected simple connected graphs $G$ and $G'$. Each graph has $N$ vertices numbered from $1$ to $N$ and $N$ edges.

Determine whether the two graphs are isomorphic. That is, decide whether a permutation $(p_1, p_2, \dots, p_N)$ of $(1, 2, \dots, N)$ exists such that for every pair of vertices $u$ and $v$, $G$ has an edge between $u$ and $v$ if and only if $G'$ has an edge between $p_u$ and $p_v$.

The first line contains one integer $N$ ($3 \le N \le 2 \times 10^5$).

Each of the next $N$ lines contains two integers $a_i$ and $b_i$ ($1 \le a_i, b_i \le N$), meaning that $G$ has an undirected edge between vertices $a_i$ and $b_i$.

Each of the following $N$ lines contains two integers $c_i$ and $d_i$ ($1 \le c_i, d_i \le N$), meaning that $G'$ has an undirected edge between vertices $c_i$ and $d_i$.

Both graphs are connected, and neither has self-loops or double edges.

N
a_1 b_1
...
a_N b_N
c_1 d_1
...
c_N d_N

Print Yes if $G$ and $G'$ are isomorphic, and No otherwise.