Forest Queries II

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