Forest Queries

You are given an n \times n grid representing the map of a forest. Each square is either empty or contains a tree. The upper-left square has coordinates (1,1), and the lower-right square has coordinates (n,n). Your task is to process q queries of the form: how many trees are inside a given 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. Each line has four integers y_1, x_1, y_2, x_2 corresponding to the corners of a rectangle.

Output

Print the number of trees inside each rectangle.

Constraints

$1 \le n \le 1000$

$1 \le q \le 2$ \cdot 10^5$

$1 \le y_1 \le y_2 \le n$

$1 \le x_1 \le x_2 \le n$

Example

Input

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

Output

3
1
2