Network Queries in Directed Graphs

You are given a directed graph with n nodes (numbered from 1 to n). Initially, the graph is empty. You are then given q queries which modify the graph or ask questions about its connectivity.

Each query is one of the following four types:

• A u v: Add a directed edge from node u to node v.
• R u v: Remove the directed edge from node u to node v (if it exists).
• D u v: Check if there is a direct edge from node u to node v. Output YES if it exists, or NO otherwise.
• P u v: Check if there is a path (possibly through intermediate nodes) from node u to node v. Output YES if such a path exists, or NO otherwise.

The queries of type A and R modify the graph but do not require an output. The queries of type D and P require you to print an answer.

Note: When checking for a path (query type P), you may use any method (such as DFS or BFS). If a query asks for a direct connection (query type D), only check if the edge from u to v exists immediately.

Input and Output are handled through standard input and standard output.

inputFormat

The input is read from standard input. The first line contains two integers n and q separated by a space, where n is the number of nodes and q is the number of queries.

Each of the next q lines contains a query in one of the following formats:

• A u v
• R u v
• D u v
• P u v

Here, u and v are integers representing node numbers.

outputFormat

For each query of type D or P, output a single line containing either YES or NO. The answers must be printed in the order the queries appear.

## sample

5 7
A 1 2
A 2 3
D 1 2
P 1 3
R 1 2
D 1 2
P 1 3

YES
YES
NO
NO

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