Matrix Path

Have the function MatrixPath(strArr) take the strArr parameter being passed which will be a 2D matrix of 0 and 1's of some arbitrary size, and determine if a path of 1's exists from the top-left of the matrix to the bottom-right of the matrix while moving only in the directions: up, down, left, and right. If a path exists your program should return the string true, otherwise your program should return the number of locations in the matrix where if a single 0 is replaced with a 1, a path of 1's will be created successfully. If a path does not exist and you cannot create a path by changing a single location in the matrix from a 0 to a 1, then your program should return the string not possible. For example: if strArr is ["11100", "10011", "10101", "10011"] then this looks like the following matrix:

1 1 1 0 0
1 0 0 1 1
1 0 1 0 1
1 0 0 1 1

For the input above, a path of 1's from the top-left to the bottom-right does not exist. But, we can change a 0 to a 1 in 2 places in the matrix, namely at locations: [0,3] or [1,2]. So for this input your program should return 2. The top-left and bottom-right of the input matrix will always be 1's.

Examples

Input: ["10000", "11011", "10101", "11001"]
Output: 1

Input: ["1000001", "1001111", "1010101"]
Output: not possible