One-Way Roads

The capital of Byteland suffers from severe traffic congestion, so the city authorities have decided to make every street one-way. If the directions are chosen carelessly, some junctions may become unreachable from others.

The transport department has prepared a list of pairs of junctions that must stay connected after the change. For each pair $(p, q)$, once every street has been made one-way it must still be possible to travel from junction $p$ to junction $q$.

Write a program that decides whether it is possible to assign a direction to every street so that all of these requirements are satisfied.

The first line contains three integers $n$, $m$, and $k$ ($1 \le n \le 50\,000$, $0 \le m, k \le 200\,000$): the number of junctions, the number of streets, and the number of requirements. Junctions are numbered from $1$ to $n$.

Each of the next $m$ lines contains two integers $a_i$ and $b_i$ ($1 \le a_i, b_i \le n$, $a_i \ne b_i$), describing a two-way street between junctions $a_i$ and $b_i$. There is at most one street between any pair of junctions.

Each of the next $k$ lines contains two integers $p_i$ and $q_i$ ($1 \le p_i, q_i \le n$, $p_i \ne q_i$), meaning that after every street is made one-way it must be possible to travel from $p_i$ to $q_i$.

Print YES if every street can be made one-way so that all requirements are satisfied, and NO otherwise.