Minimum Walls to Remove

You are given an n x n grid where each cell is initially filled with a wall (represented by the character #). Your task is to determine the minimum number of walls to remove in order to create a path from the top-left corner (0, 0) to the bottom-right corner (n-1, n-1). The path can move only horizontally or vertically between adjacent cells.

If it is impossible to create such a path, output no path.

The optimal strategy, when a path is possible, is to remove exactly 2(n-1) - 1 walls. However, note that for n = 2 the task is impossible, so the answer should be no path.

Examples:

• For n = 4: The minimum walls to remove is 5.
• For n = 3: The minimum walls to remove is 3.
• For n = 2: There is no path, so the answer is no path.
• For n = 100: The minimum walls to remove is 197.
• For n = 5: The minimum walls to remove is 7.

Mathematically, for n > 2, the answer can be written in LaTeX as:

$$\text{Minimum Walls Removed} = 2(n - 1) - 1$$

inputFormat

The input consists of a single integer n on one line, representing the dimension of the grid.

outputFormat

Output a single line which is either the minimum number of walls to remove (an integer) or the string no path if a valid path cannot be created.

## sample

4

5