Painting vertices

You are given a directed graph, where some vertices are initially painted and some are not, and two vertices $x$ and $y$ . Please paint the minimum number of additional vertices so that there is a path from $x$ to $y$ that only passes through painted vertices.

Input

Input consists of several cases. Every case begins with the number of vertices $n$ , the starting vertex $x$ and the final vertex $y$ . Next comes a number $m$ , followed by $m$ different arcs $u$ $v$ where $u \ne v$ . Follow a number $p$ , followed by the $p$ vertices initially painted. Assume $2 \le n \le 10^4$ , $x \ne y$ , $0 \le m \le 5n$ , and $0 \le p \le n$ . The vertices are numbered starting at 0.

Output

For every case, print the minimum number of vertices to paint so that there is a path from $x$ to $y$ that only passes through painted vertices, $x$ and $y$ included. If it is impossible, state so.

Problem information

Author: Salvador Roura

Generation: 2026-01-25T11:52:30.123Z