Let us consider an undirected graph G = < V, E >. At first there is no edge in the graph. You are to write a program to calculate the connectivity of two different vertices. Your program should maintain the functions inserting or deleting an edge.

The first line of the input contains an integer numbers N (2 <= N <= 1000) -- the number of vertices in G. The second line contains the number of commands Q (1 <= Q <= 20000). Then the following Q lines describe each command, and there are three kinds of commands:

I u v: Insert an edge (u, v). And we guarantee that there is no edge between nodes u and v, when you face this command.
D u v: Delete an existed edge (u, v). And we guarantee that there is an edge between nodes u and v, when you face this command.
Q u v: A querying command to ask the connectivity between nodes u and v.

You should notice that the nodes are numbered from 1 to N.

Output one line for each querying command. Print "Y" if two vertices are connected or print "N" otherwise.

3 
7
Q 1 2
I 1 2
I 2 3
Q 1 3
D 1 2
Q 1 3
Q 1 1

N
Y
N
Y

POJ Monthly--2006.06.25, Zheng Zhao