Square Searching

There are a total of n x n squares, n rows vertically and n columns horizontally. Some squares are marked. Create a program that reads the marked state of each square and displays the length of the side of the largest square consisting of only the unmarked squares as an output.

For example, each dataset is given the following data:

Ten ... * .... ** .......... ** .... ** .. ........ *. .. * ....... .......... . * ........ .......... .... * .. *** . * .... * ...

One line of input data represents the square of one line. Of the character strings in the input data,. (Period) indicates unmarked squares, and * (asterisk) indicates marked squares.

In the above example, the square indicated by 0 in the figure below is the largest.

... * .... ** .......... ** .... ** .. ... 00000 *. .. * 00000 .. ... 00000 .. . * .00000 .. ... 00000 .. .... * .. *** . * .... * ...

Therefore, if you output 5, the answer will be correct.

If all the squares are marked, output 0.

Input

Multiple datasets are given in the above format. When n is 0, it is the last input. n is 1000 or less. The input data string does not contain any characters other than periods, asterisks, and line breaks. The number of datasets does not exceed 50.

Output

For each dataset, output the length (integer) of the side of the largest square on one line.

Example

Input

10 .......** .......... ...... ......... ......... .......... ......... .......... ......** ........ 10 .* ....... ..... ........ ....* .......... .* ....... **..... ....... 0

Output

5 3

inputFormat

outputFormat

output.

For example, each dataset is given the following data:

Ten ... * .... ** .......... ** .... ** .. ........ *. .. * ....... .......... . * ........ .......... .... * .. *** . * .... * ...

One line of input data represents the square of one line. Of the character strings in the input data,. (Period) indicates unmarked squares, and * (asterisk) indicates marked squares.

In the above example, the square indicated by 0 in the figure below is the largest.

... * .... ** .......... ** .... ** .. ... 00000 *. .. * 00000 .. ... 00000 .. . * .00000 .. ... 00000 .. .... * .. *** . * .... * ...

Therefore, if you output 5, the answer will be correct.

If all the squares are marked, output 0.

Input

Multiple datasets are given in the above format. When n is 0, it is the last input. n is 1000 or less. The input data string does not contain any characters other than periods, asterisks, and line breaks. The number of datasets does not exceed 50.

Output

For each dataset, output the length (integer) of the side of the largest square on one line.

Example

Input

10 .......** .......... ...... ......... ......... .......... ......... .......... ......** ........ 10 .* ....... ..... ........ ....* .......... .* ....... **..... ....... 0

Output

5 3

样例

10
...*....**
..........
**....**..
........*.
..*.......
..........
.*........
..........
....*..***
.*....*...
10
****.*****
*..*.*....
****.*....
*....*....
*....*****
..........
****.*****
*..*...*..
****...*..
*..*...*..
0

5
3

</p>