Code Submission Evaluation System Login

CSES Problem Set

Graph Girth


Task | Statistics


CSES - Graph GirthCSES - 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
Example

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


Output:
3