Graph Girth

• Time limit: 1.00 s
• Memory limit: 512 MB

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

Input

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.

Output

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

Constraints

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

Example

Input:
5 6
1 2
1 3
2 4
2 5
3 4
4 5

Output:
3