P8220 [WFOI - 02] I wanna win the race (Race).

> best is yet to come Kid accidentally entered online mode. He needs to clear the level faster than his opponent to win.

Kid enters a venue where several players are racing. The venue can be abstracted as a coordinate system. The players need to run from $(1, 1)$ to $(n, n)$. If a player is currently at $(x, y)$, then in the next step they can move to $(x \pm 1, y)$ or $(x, y \pm 1)$. Note that they **can only move in the first quadrant**, meaning $x > 0, y > 0$ at all times. All points are initially type $\texttt{A}$. The organizer chooses a triple $(a, b, c)$ and changes all points $(x, y)$ satisfying $a \le x \le b$ and $y \le c$ into type $\texttt{B}$. Each time a player passes a type $\texttt{A}$ point it takes $1$ second, and each time they pass a type $\texttt{B}$ point it takes $2$ seconds. Please note that **the starting point and the ending point are also included in the calculation.** Kid wants to win this race, and he wants to know the **minimum** number of seconds needed to reach the destination. **Please note that there are important constraints in the Constraints section.**

There are two lines. The first line contains an integer $n$. The second line contains three integers $a, b, c$.

Output one integer, representing the minimum number of seconds Kid needs to clear the level.

**Sample Explanation** The figure below shows one feasible plan. Purple points are type $\texttt{A}$ points, and red points are type $\texttt{B}$ points:  **Constraints** **This problem uses bundled $\tt Subtask$ tests.** For $30\%$ of the testdata, $1 < a < b < n \le 10^3, 0 < c \le 10^3$. For $100\%$ of the testdata, $1 < a < b < n \le 10^9, 0 < c \le 10^9$. Translated by ChatGPT 5