You are given a 2 by n grid, where the cell on row i column j contains a non-negative number ai,j . You can start at either cell in the lefttmost column, and your goal is to reach either cell in the rightmost column by a sequence of moves. You can move to an adjacent cell (if it exists) in each of the 4 cardinal directions (up, down, left and right). A path achieves a score equal to the sum of values in its cells. Note that a cell which is used twice in a path only counts its value once to the score of that path. Design an algorithm which runs in O(n) time and finds a path of minimum score from the leftmost column to the rightmost column.

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Topological Sort

Topological sort is a sorting technique that sets up a hierarchy in a process. In this technique, when a directed network has nodes connected by arrows, the root node is placed before the successor node.