### Problem Statement

You will be given a map of the bunker. The map will consist of bombs ('*'), empty cells ('.') and secret objects ('?') arranged on a regular grid. For security reasons, in case of danger, all secret objects in the bunker should be destroyed by the explosion of any one bomb. A bomb explosion destroys all objects in range D, where D depends on the bomb type. A bomb explosion also causes all other bombs in range D to explode. More formally, an item (a secret object or a bomb) will be affected by a bomb explosion if the distance between the centers of their cells is not greater than D.

You will be given a String[] field. Return the minimal value of D that will ensure that all secret objects will be destroyed by the explosion of any one bomb.

### Definition

 Class: SecurityBunker Method: chooseBomb Parameters: String[] Returns: double Method signature: double chooseBomb(String[] field) (be sure your method is public)

### Notes

-The returned value must be accurate to 1e-9 relative or absolute.

### Constraints

-field will contain between 1 and 50 elements, inclusive.
-Each element of field will contain between 1 and 50 characters, inclusive.
-Each element of field will contain the same number of characters.
-field will contain only the characters '*', '.', and '?'.
-field will contain between 1 and 100 '*' characters, inclusive.
-field will contain between 1 and 100 '?' characters, inclusive.

### Examples

0)

 ```{"*.*", ".?.", "*.*"}```
`Returns: 1.4142135623730951`
 The answer is the distance from the secret object to any one of the bombs.
1)

 ```{"*****", ".?.?.", "..?..", ".?.?.", "*****"}```
`Returns: 3.0`
 With D>=1, the explosion of any bomb will explode all other bombs in the same row.
2)

 ```{"*****", "....*", "....*", ".?..*", "....*", "*...*", "*****"}```
`Returns: 2.23606797749979`
3)

 ```{"*.*.*.*", ".?.?.?."}```
`Returns: 2.0`
 D=2 is enough to explode all bombs and the secret objects with them.
4)

 ```{"?*..*?....?", "...........", "....*......", "...?.......", ".*....**?..", "*......?...", ".......*...", ".......?.*.", "..*.......*", "?........?.", "......?*?.."}```
`Returns: 5.0`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=4650

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=8002&pm=4650

Andrew_Lazarev

#### Testers:

PabloGilberto , brett1479 , Olexiy

Graph Theory