I have got some impossible queries for you! (or are they? ;) )

You have n binary numbers of length m. The ith binary number is B_i. Also, you have to perform q queries on them. The indexing is zero-based and the indexing of bits starts from left.

The queries are of type : a i j. If a is:

• 0 : perform Logical AND operation between B_i and B_j and output number of 1s in the result.
• 1 : perform Logical OR operation between B_i and B_j and output number of 1s in the result.
• 2 : perform Logical XOR operation between B_i and B_j and output number of 1s in the result.
• 3 : flip the value of the jth bit of B_i, i.e, make the bit 0 if it is 1 and vice-versa.

Note : For queries of type 0, 1, and 2, the binary numbers remain unchanged.

It is also recommmended to use Fast I/O for C++ and JAVA programmers.

Input Format

• First line contains Integers n and m
• The next n lines contains binary numbers of length m. The ith line contains binary number B_i
• The next line contains an integer q
• The next q lines contain queries of type : a i j.

Output Format

• Output number of 1s in the result of type 0, 1 and 2 queries.

Constraints

$1 \le \mathbf{n,m} \le 2500$

$0 \le \mathbf{a} \le3$

$0 \le \mathbf{i} \lt \mathbf{n}$

$0 \le \mathbf{j} \lt \mathbf{m}$

$1 \le \mathbf{q} \le 10^6$ (As usual i have kept a few 'easy' test cases to boost your confidence, but try to get 100 points! :) )