You are given a connected undirected graph containing $N$ nodes and $M$ edges. The task is very simple. You are provided two nodes $u$ and $v$. You are required to check whether the path from $u$ to $v$ is unique or not. If there exists a path, you are required to determine the distance between the nodes $u$ and $v$, then print $-1$. You must perform these operations for $Q$ queries. 

Input format

• First line: Two space-separated integers$N$ and $M$ 
• Next $M$ lines: Two space-separated integers $u$ and $v$ denoting that there is an edge between node $u$ and $v$
• Next line contains a single integer $Q$  denoting the number of queries
• Next $Q$ lines: Two space-separated integers $u$ and $v$

Output format

For each query, print the distance between the two nodes if there exists a unique path between the nodes in that query. Otherwise, print $-1$.

Constraints

$2 \le N \le 10^5\\ N - 1 \le M \le min(10^5, \frac{N * (N - 1)}{2})\\ 1 \le u, v \le N$$\\ 1 \le Q \le 10^5$

The provided graph is connected and it does not contain self-loops and multiple edges.