Given an undirected graph, your task is to determine its girth , i.e., the length of its shortest cycle.

The first input line has two integers $n$ and $m$ : the number of nodes and edges. The nodes are numbered $1,2,\dots,n$ .

After this, there are $m$ lines describing the edges. Each line has two integers $a$ and $b$ : there is an edge between nodes $a$ and $b$ .

You may assume that there is at most one edge between each two nodes.

• $1 \le n \le 2500$
• $1 \le m \le 5000$

Print one integer: the girth of the graph. If there are no cycles, print $-1$ .