Waypoints

题目描述

You are given a connected, undirected, unweighted simple graph with $n$ vertices and $m$ edges (no self-loops, no multiple edges). You are also given $k$ distinct waypoint vertices.

A simple cycle is a sequence of distinct vertices in which consecutive vertices are joined by an edge, including the first vertex and the last vertex; its length is its number of vertices. Moreover, we require that every cycle has length at least 3.

Find the minimum possible length of a simple cycle that passes through all $k$ waypoints, or report that no such path exists.

输入格式

The first line contains an integer $T$ — the number of test cases.

Each test case: the first line has $n$, $m$, $k$ ($1 \le n \le 50$, $n-1 \le m \le \binom{n}{2}$, $1 \le k \le \min(n,12)$). Each of the next $m$ lines has an edge $u$ $v$ ($1 \le u,v \le n$, $u \ne v$); the graph is simple and connected. The last line lists the $k$ distinct waypoints.

It is guaranteed that the sum of $2^k$ over all test cases does not exceed $2^{12}$.

输出格式

For each test case, print one line: the minimum number of edges of a simple cycle through all $k$ waypoints, or $-1$ if none exists.

样例输入 #1

2
4 4 2
1 2
2 3
3 4
1 4
1 4
4 3 3
1 2
1 3
1 4
2 3 4

样例输出 #1

4
-1