Police Stations

There are $N$ police stations in Flatland, and the $i$-th police station is at coordinate $(x_i, y_i)$. The authority wants to increase cooperation among these police stations by reducing the miscommunication that often arises between them. To do this, the authority decides to build a new tower that will serve as the Communication Control Center (CCC). The CCC can only be built at $(x, y)$ where both $x$ and $y$ are integers. It does not matter whether a police station already occupies $(x, y)$; the CCC can be built alongside that police station.

The CCC then draws a communication cable to each police station, with some restrictions.

• Each cable serves only one police station, so serving $N$ police stations requires $N$ cables.
• A cable can only be laid parallel to the $x$-axis or the $y$-axis. Diagonal crossing is not allowed.

Because of a strange physics law in Flatland, each cable can have length at most $L$ in the $x$-axis direction and at most $W$ in the $y$-axis direction. This is why such a cable is called an $\langle L, W \rangle$ cable in Flatland. For stable communication, all police stations must be connected by the same type of cable.

Recent advances in science and technology in Flatland let physicists build an $\langle L, W \rangle$ cable for any $L$ and $W$ they like, at a cost. The cost becomes very expensive for larger $L$ and $W$, so the authority must find $L$ and $W$ that satisfy their need, connecting all police stations to the CCC, while minimizing the value of $L + W$.

In this problem, you must find $L$ and $W$ such that $L + W$ is minimized, the authority can build the CCC at $(x, y)$ where both $x$ and $y$ are integers, and all police stations can be connected to the CCC with $\langle L, W \rangle$ cables. If there are multiple solutions, minimize $L$ first, and then minimize $W$.

The first line contains an integer $N$ ($1 \le N \le 100\,000$), the number of police stations in Flatland. Each of the next $N$ lines contains two integers $x_i$ $y_i$ ($-10^6 \le x_i, y_i \le 10^6$), the location of a police station.

Output two integers $L$ and $W$ separated by a single space, such that $L + W$ is minimized, the authority can build the CCC at $(x, y)$ where both $x$ and $y$ are integers, and all police stations can be connected to the CCC with $\langle L, W \rangle$ cables. If there are multiple solutions, minimize $L$ first, and then minimize $W$.