Copying Coins

Raymu is sad because he has no money, and one day he finds a machine. The machine is a square with side length $N$, made of $1 \times 1$ cells. Cells are addressed by coordinates: the bottom-left cell is $(1, 1)$ and the top-right cell is $(N, N)$. At the start, only the cell $(x, y)$ has a coin, and all other cells are empty. Here $(x, y)$ is the cell $x-1$ steps right and $y-1$ steps up from $(1, 1)$.

Raymu can run the machine once in one of four directions: up, down, left, or right. Every coin in the machine moves in the direction the machine runs, and new coins appear along the path each coin travels. Raymu wants to fill every cell of the machine with coins, and he wants to minimize the number of runs. Given the side length and the starting position of the coin, find the minimum number of runs needed to fill every cell.

The first line contains the side length $N$ of the machine. ($1 \leq N \leq 5\ 000$)

The second line contains two integers $x$ and $y$ separated by a space, the starting position of the coin. ($1 \leq x, y \leq N$)

Print the minimum number of machine runs.