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

*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`