You are given a 2D character array denoting forest of length N and breadth M . In the matrix, '.' denotes barren land and ' * ' denotes tree.
You are given Q questions. In each question, you are given integer K and you have to determine the number of unique squares of side less than or equal to K which contain only trees.

Input

First line : N and M (N denoting number of rows and M denoting number of columns).

Each of the next N lines contains string of M length containing '.' and '*' .

Next line consists of an integer Q, denoting number of questions.

Each of the next Q lines contains a single integer K.

Input Constraints

\(1 \le N, M \le 1000\)
\(1 \le Q \le 10^5\)
\(0 \le K \le 10^3\)

Output

For each question, print the number of unique squares of side less than or equal to K which contain only trees. Answer for each question should come in a new line.