### Problem Statement

You will be given a list of patterns. Each pattern will contain only digits ('0'-'9'), question marks ('?'), and may potentially begin or end (but not both) with a hyphen ('-'). You must return the number of strings of length len that match all of the patterns. A digit must be matched with the same digit. A question mark can be matched with any digit. If the pattern ends with a hyphen, the pattern is describing a prefix. Similarly, if the pattern begins with a hyphen it describes a suffix. If there are no hyphens, the matched string must have the same length as the pattern. Said differently, a hyphen matches 0 or more digits.

### Definition

 Class: DigitMask Method: howMany Parameters: String[], int Returns: int Method signature: int howMany(String[] patterns, int len) (be sure your method is public)

### Constraints

-patterns will contain between 1 and 50 elements, inclusive.
-Each element of patterns will contain between 1 and 50 characters, inclusive.
-Each character in patterns will be a digit ('0'-'9'), a question mark ('?'), or a hyphen ('-');
-Each element of patterns will contain at most 1 hyphen, and it must occur at the beginning or the end of the element.
-len will be between 1 and 50, inclusive.
-The return value will be between 0 and 1,000,000,000, inclusive.
-No element of patterns will be "-" (quotes for clarity).

### Examples

0)

 `{"???"}` `3`
`Returns: 1000`
 Every 3 digit string is possible.
1)

 `{"9??","??7"}` `3`
`Returns: 10`
 The first digit must be 9 and the last must be 7.
2)

 `{"9??","??7"}` `4`
`Returns: 0`
 The patterns say that the string must have length 3.
3)

 `{"9??-","-???7"}` `4`
`Returns: 100`
 The first pattern says the string begins with a 9 and has at least 3 digits. The second pattern says the string ends with a 7 and has at least 4 digits.
4)

 ```{ "??????????????????????????????????????????????????", "?????????????????????????????????????????????????9", "?????????????????????????????????????????????????8" }``` `50`
`Returns: 0`
5)

 ```{ "-?????" }``` `4`
`Returns: 0`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=7518

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=10706&pm=7518