Given a graph with vertices divided into N groups, each containing \(2^M\) vertices that are numbered from 0 inside the group.
Initially there is no edge. There are Q queries. Each query will be of one of the following 3 types:
\(1 \space i \space j \; p\): For every vertex numbered x from 0 to \(2^m-1\) add an edge between vertex x from group i and vertex \(x \oplus p\) from group j.
\(2 \; i \; x\): Find the size of component containing vertex x in group i.
3: Count the total number of connected components.

Input Format:
First line consists of three space separated integers denoting N, M and Q.
Q lines follow, each containing one of the given 3 types of queries.

Output Format:
For every query of type 2 and 3 print the required answer in a new line.

Constraints:
\(1 \le N \le 10^5\)
\(1 \le M \le 40\)
\(1 \le Q \le 4 \times 10^5\)
\(0 \le p, x \le 2^M-1\)
\(1 \le i, j \le N\)