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:

1. Change the state (empty/tree) of a square.
2. 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