Dijamant

Lovro has a table of $n$ rows and $m$ columns, where each cell is either . or #. By rotating a square by 45◦ a diamond shape is formed in the table. For a part of the table to be considered a diamond, its edge must also consist only of the character #, while its inside must be completely filled with . and it must be nonempty. Outside of a diamond any character is allowed. Diamonds come in different sizes, and the three smallest examples of a diamond are shown in the first sample.

Fabijan asked Lovro to tell him how many diamonds are there in the table, or else Lovro has to give him a cookie. Help Lovro by writing a program which counts the number of diamonds in his table.

The first line contains positive integers $n$ and $m$ ($1 ≤ n, m ≤ 2000$), the number of rows and columns. Each of the next $n$ lines contains $m$ characters . or # which describe the table.

In the only line print the number of diamonds in the table.

Clarification of the second example:

There is only one diamond in the table (the one with the smallest possible size). There appears to be another diamond containing it, but it is not considered a diamond because its inside is not completely filled with '.'. The shape on the right side of the table is also not a diamond because it’s missing a # character on its edge.