**Time limit:**1.00 s**Memory limit:**512 MB

You are given an n \times n grid representing the map of a forest. Each square is either empty or has a tree. Your task is to process q queries of the following types:

- Change the state (empty/tree) of a square.
- How many trees are inside a rectangle in the forest?

# Input

The first input line has two integers n and q: the size of the forest and the number of queries.

Then, there are n lines describing the forest. Each line has n characters: `.`

is an empty square and `*`

is a tree.

Finally, there are q lines describing the queries. The format of each line is either "1 y x" or "2 y_1 x_1 y_2 x_2".

# Output

Print the answer to each query of the second type.

# Constraints

- 1 \le n \le 1000
- 1 \le q \le 2 \cdot 10^5
- 1 \le y,x \le n
- 1 \le y_1 \le y_2 \le n
- 1 \le x_1 \le x_2 \le n

# Example

Input:

4 3 .*.. *.** **.. **** 2 2 2 3 4 1 3 3 2 2 2 3 4

Output:

3 4