Design an algorithm to find the shortest part through a grid(matrix). The function (algorithm) will take an m*n matrix as an input, whose entries are the corresponding costs of landing on it. For example, the following matrix (grid) is an input:

We always need to find the shortest part from the left bottom to the right up point. The valid move is up, right, down and left. In this example, the correct answer should be [[3,0],[3,1],[3,2],[3,3],[2,3],[1,3],[0,3]] (from [3,0] to [0,3] ).

When there is a tie, break the tie according to the following order (up, right, down, left).

0 | 1 1 2 3 3 | 7| 2 0 | 1 1 2 3 3 | 7| 2