Each test consists of several sets of input data. The first line contains a single integer $t$ ($1 \le t \le 10\,000$) --- the number of input data sets. The following describes the input data sets.

The first line of each data set contains an integer $n$ ($1 \le n \le 200\,000$) --- the number of lifeboats in the machine.

The next $n$ lines follow. The $i$-th of them contains two integers $x_i$, $y_i$ ($-10^9 \le x_i, y_i \le 10^9$) --- the coordinates of the $i$-th lifeboat.

In the penultimate line of each data set, there are two integers $a_x$, $a_y$ ($-10^9 \le a_x, a_y \le 10^9$) --- the coordinates of point $A$.

In the last line of each data set, there are two integers $b_x$, $b_y$ ($-10^9 \le b_x, b_y \le 10^9$) --- the coordinates of point $B$.

It is guaranteed that points $A$ and $B$ do not coincide. It is guaranteed that all lifeboats in each input data set are located at pairwise distinct points.

Let $N$ denote the sum of $n$ across all input data sets. It is guaranteed that $N$ does not exceed $200\,000$.