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.