Please solve the programming task below using a self-contained code snippet in a markdown code block.

Given an m x n grid. Each cell of the grid has a sign pointing to the next cell you should visit if you are currently in this cell. The sign of grid[i][j] can be:

1 which means go to the cell to the right. (i.e go from grid[i][j] to grid[i][j + 1])
2 which means go to the cell to the left. (i.e go from grid[i][j] to grid[i][j - 1])
3 which means go to the lower cell. (i.e go from grid[i][j] to grid[i + 1][j])
4 which means go to the upper cell. (i.e go from grid[i][j] to grid[i - 1][j])

Notice that there could be some signs on the cells of the grid that point outside the grid.
You will initially start at the upper left cell (0, 0). A valid path in the grid is a path that starts from the upper left cell (0, 0) and ends at the bottom-right cell (m - 1, n - 1) following the signs on the grid. The valid path does not have to be the shortest.
You can modify the sign on a cell with cost = 1. You can modify the sign on a cell one time only.
Return the minimum cost to make the grid have at least one valid path.
 
Please complete the following python code precisely:
```python
class Solution:
    def minCost(self, grid: List[List[int]]) -> int:
```