Problem Statement  
Manao has an N x M matrix filled with digits. The rows in the matrix are consecutively numbered from 0 to N1 starting from the top row and the columns are numbered from 0 to M1 starting from the left column. He wants to perform several matrix shift operations in order to obtain a matrix with value in the upper left corner. There are four types of matrix shifts: left, right, top and bottom. Performing the left shift on the matrix, we shift each of its columns one position to the left and put the first column in place of the last one. Similarly, right shift results in shifting each column to the right and placing the last one in place of the first. Top shift takes each row one position up and puts the first row in place of the last, and bottom shift shifts all the rows one position down and puts the last row in place of the first row. Note that if a matrix has only one row, then top and bottom shifts do not change the matrix in any way. Similarly, if a matrix has a single column, then right and left shifts have no effect. You are given a String[] matrix, where the jth character of the ith element is the digit in row i, column j. Compute and return the minimum possible total number of shifts that Manao should perform to accomplish his task. If there is no way to obtain a matrix with the upper left element equal to value, return 1 instead.  
Definition  
 
Constraints  
  matrix will contain between 1 and 50 elements, inclusive.  
  Each element of matrix will contain between 1 and 50 characters, inclusive.  
  All elements of matrix will have the same length.  
  matrix will contain digits ('0''9') only.  
  value will be between 0 and 9, inclusive.  
Examples  
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