Ancient Greek Isomorphism

Zeus's favorite graph is the square grid graph. It is an undirected graph shaped as a grid with $n$ rows and $m$ columns, with $n \cdot m$ vertices and $n \cdot (m - 1) + (n - 1) \cdot m$ edges. Each grid point is joined to its adjacent grid points.

$(i, j)$ denotes the vertex at the intersection of row $i$ and column $j$. Formally, there is an edge between $(i, j)$ and $(i+1, j)$ for all $(1 \leq i < n, 1 \leq j \leq m)$, and an edge between $(i, j)$ and $(i, j+1)$ for all $(1 \leq i \leq n, 1 \leq j < m)$.

(The picture shows a $6 \times 5$ square grid graph.)

Surprisingly, Poseidon's favorite graph is also undirected, also has $n \cdot m$ vertices and $n \cdot (m - 1) + (n - 1) \cdot m$ edges, and has no self-loops or multiple edges. Its vertices are numbered with integers from $1$ to $n \cdot m$.

Poseidon wants to know whether the two graphs are isomorphic. Formally, can each vertex of Poseidon's graph be paired with exactly one vertex of Zeus's graph, covering every vertex of both graphs exactly once, so that two vertices are adjacent in one graph if and only if their partners are adjacent in the other? Help Poseidon decide.

The first line contains two integers $n, m$, the dimensions of the grid ($2 \leq n, m, n \cdot m \leq 2 \cdot 10^{5}$).

Each of the next $n \cdot (m - 1) + (n - 1) \cdot m$ lines describes an edge of Poseidon's graph with two integers $u_i, v_i$ ($1 \leq u_i, v_i \leq n \cdot m$, $u_i \neq v_i$). It is guaranteed that Poseidon's graph has no multiple edges.

If Poseidon's graph and Zeus's graph are isomorphic, print Yes. Otherwise, print No. The answer may be in any letter case.

The graph from the second example is shown in the picture below.