Fewest Arrow Changes Creating a Corner-to-Corner Path

### Problem Each grid cell has an arrow:1 right,2 left,3 down,4 up. Some arrows may point outside the grid. Starting at the top-left, follow arrows to the bottom-right. You may change each cell's arrow at most once for cost 1. Return the minimum total change cost that permits at least one such path; the path need not minimize steps. ```cpp class Solution { public: int minCost(vector<vector<int>>& grid); }; ``` ### Examples **Example 1:** ```text Input: grid = [[1,3],[1,4]] Output: 0 Explanation: Follow right,then down to reach the bottom-right without changing any arrow. ``` **Example 2:** ```text Input: grid = [[2,2]] Output: 1 Explanation: Change the first arrow from left to right; the destination's outgoing arrow does not matter. ``` ### Constraints - The rectangular grid has 1 to 100 rows and 1 to 100 columns. - Every sign is an integer from 1 through 4 with the stated directions. ### Contract considerations Only the minimum cost is returned. Multiple routes do not create output freedom in this numeric result. ```hint Read the boundary condition Distinguish modification cost from path length. Check outward-pointing arrows and a grid whose start is already the destination. ``` ### Boundary reminders Only the minimum cost is returned. Multiple routes do not create output freedom in this numeric result.