Surveillance Cameras

Changyoung wants to monitor all of his $N$ cows ($1 \le N \le 50{,}000$) using three newly purchased surveillance cameras.

The $i$-th cow is located at $(x_i, y_i)$, where $x_i$ and $y_i$ are integers with $0 \le x_i, y_i \le 1{,}000{,}000{,}000$. No two cows share the same coordinates.

Each surveillance camera monitors every cow that lies on a single vertical line or a single horizontal line. In other words, one camera covers an entire column $x = a$ or an entire row $y = b$.

Write a program that determines whether all cows can be monitored using three cameras. Equivalently, decide whether the $N$ points in the plane can all be covered by three axis-parallel lines.

The first line contains the number of cows $N$.

Each of the next $N$ lines contains the coordinates $x_i$ and $y_i$ of a cow, separated by a space.

Print $1$ if all cows can be monitored with three surveillance cameras, and $0$ otherwise.

Suppose there are $6$ cows located at $(1,7)$, $(0,0)$, $(1,2)$, $(2,0)$, $(1,4)$, and $(3,4)$. Placing the cameras at $y = 0$, $x = 1$, and $y = 4$ monitors every cow, so the answer is $1$.