Tour de Byteotia

There are $n$ towns in Byteotia. Some pairs of towns are joined by bidirectional roads. The roads meet only at their endpoints and never cross (a system of tunnels and flyovers makes this possible).

A famous bicycle race is about to be held. Its route follows some of the roads, starts and ends in the same town, and travels along each road at most once. In other words, the route is a closed trail that reuses no road.

Byteasar and his club friends dislike the race and want to keep it away from the towns where they live. Given the towns where the club members live, determine the minimum number of roads that must be blocked so that the race's route cannot pass through any of those towns.

The first line contains three integers $n$, $m$, and $k$ ($1 \le n \le 10^6$, $0 \le m \le 2 \cdot 10^6$, $1 \le k \le n$), separated by single spaces: the number of towns, the number of roads, and the number of towns where club members live. The towns are numbered from $1$ to $n$, and the towns where club members live are exactly those numbered from $1$ to $k$.

Each of the next $m$ lines contains two integers $a_i$ and $b_i$ ($1 \le a_i < b_i \le n$), separated by a single space, meaning that towns $a_i$ and $b_i$ are joined by a bidirectional road. Every pair of towns is joined by at most one road.

Print a single integer: the minimum number of roads that must be blocked so that the race's route cannot pass through any town where a club member lives.