AT_past18_h Cを探せ！

An object on a grid like these is called a **C**. ``` ### #### ##### #.. #... #.... ### #... #.... #### #.... ##### ``` Illustrated above are **C**s of level $ 1 $ , $ 2 $ , and $ 3 $ , from left to right. Formally, for a positive integer $ l $ , a **C**\* of level $ l $ is defined as follows. - A **C** of level $ l $ is an $ (l+2) \times (l+2) $ square grid. - Every cell on the upper, left, or lower border of the square has `#` written on it. - Every other cell has `.` written on it. You are given an $ N \times N $ grid. Each cell has `#` or `.` written on it. The grid is described by $ N $ strings $ S_1,S_2,\dots,S_N $ ; the $ j $ -th character of $ S_i $ represents the character written on the cell in the $ i $ -th row from the top and $ j $ -th column from the left. Find the maximum level of a **C** that can be obtained by extracting a (connected) square from this grid. If no square extracted from the grid forms a **C**, print $ 0 $ .

The input is given from Standard Input in the following format: > $ N $ $ S_1 $ $ S_2 $ $ \vdots $ $ S_N $

Print the answer as an integer.

### Sample Explanation 1 If you extract the square consisting of $ 1 $ -st through $ 3 $ -rd rows from the top and $ 2 $ -nd through $ 4 $ -th columns, it forms a **C** of level $ 1 $ . One cannot extract a **C** of level $ 2 $ or greater from this grid. ### Sample Explanation 2 One cannot extract a **C** from this grid. ### Constraints - $ N $ is an integer between $ 3 $ and $ 300 $ , inclusive. - $ S_i $ is a length- $ N $ string consisting of `#` and `.`.