You are given an undirected connected graph with $n$ vertices and $m$ edges, containing no multiple edges or self-loops.

ymqOAO has $k$ queries. For each query, determine if the graph remains connected after removing $c_i$ specific edges.

Note: Queries are independent, meaning the removal of edges in one query does not affect subsequent queries.

Definition: * Connected graph: A graph in which there is a path between any two vertices.

Input

The first line contains two integers $n$ and $m$.

The next $m$ lines each contain two positive integers $x_i, y_i$, representing the $i$-th edge connecting $x_i$ and $y_i$.

The next line contains an integer $k$, representing the number of queries.

The next $k$ lines each describe a query: the first integer $c_i$ is the number of edges to be removed, followed by $c_i$ ($1 \le c_i \le 4$) integers representing the indices of the edges to be removed. The edge indices are in the range $[1, m]$.

Output

For each query, if the graph is not connected, output 'Bob'; otherwise, output 'ymqOAO'. (Do not include the quotes.)

Examples

Input 1

4 5
1 2
2 3
3 4
4 1
2 4
3
1 5
2 2 3
2 1 2

Output 1

ymqOAO
Bob
ymqOAO

Constraints

• For 10% of the data, $1 \le m, n, k \le 2000$.
• For another 10% of the data, $m = n - 1$.
• For another 10% of the data, $c_i = 1$.
• For 60% of the data, $1 \le m, n, k \le 10^5$.
• For 100% of the data, $1 \le m, n, k \le 10^6$.