Longest Matrix Path

Have the function LongestMatrixPath(strArr) take the array of strings stored in strArr, which will be an NxM matrix of positive single-digit integers, and find the longest increasing path composed of distinct integers. When moving through the matrix, you can only go up, down, left, and right. For example: if strArr is ["345", "326", "221"], then this looks like the following matrix:

3 4 5
3 2 6
2 2 1

For the input above, the longest increasing path goes from: 3 -> 4 -> 5 -> 6. Your program should return the number of connections in the longest path, so therefore for this input your program should return 3. There may not necessarily always be a longest path within the matrix.

Examples

Input: ["12256", "56219", "43215"]
Output: 5

Input: ["67", "21", "45"