### Problem Statement

Consider a matrix with n columns, given by m, where mi,j is represented by character j of element i of m. We would like to find some function, f, such that for all i:

f(mi,0,mi,1,...,mi,n-1) = ti.

All elements of the matrix are binary 0's and 1's, as are the elements of t. Furthermore, the function must take on the form:

a0*mi,0 ^ a1*mi,1 ^ ... ^ an-1mi,n-1, where each aj is either 0 or 1 and '^' represents the XOR operation. In other words, the function takes a row of the matrix, and XORs some subset of the elements of that row to get the target from t. Your task is to return how many distinct functions (choices of ai's) give the correct target for each i.

### Definition

 Class: XORing Method: findSubset Parameters: String[], int[] Returns: long Method signature: long findSubset(String[] m, int[] t) (be sure your method is public)

### Constraints

-m and t will contain the same number of elements.
-m and t will contain between 1 and 50 elements, inclusive.
-Each element of m will contain the same number of characters.
-Each element of m will contain between 1 and 50 characters, inclusive.
-Each character in m will be '0' or '1'.
-Each element of t will be 0 or 1.

### Examples

0)

 ```{"000", "001", "010"}``` `{0,1,1}`
`Returns: 2`
1)

 ```{"000", "001", "010"}``` `{1,1,1}`
`Returns: 0`
2)

 ```{"0000", "0000", "0000"}``` `{0,0,0}`
`Returns: 16`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=4829

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=8095&pm=4829

lars2520

#### Testers:

PabloGilberto , Yarin , Olexiy

Brute Force