CSES - Datatähti Open 2019 - Function
• Time limit: 1.00 s
• Memory limit: 512 MB
A polygonal chain consists of points $p_1,p_2,\dots,p_n$ where there is a line segment between each two consecutive points.

You are given a set of polygonal chains, and your task is to find out for each chain if it can be represented as a function by rotating the figure. This means that no vertical line intersects the figure in two points.

Input

The first input line has an integer $t$: the number of polygonal chains. After this, each chain is described as follows:

The first line has an integer $n$: the number of points. After this, there are $n$ lines, each having two integers $x$ and $y$. No two consecutive points are the same, and no three consecutive points lie on the same line.

Output

For each polygonial chain, print YES if it can be represented as a function, and NO otherwise.

Example

Input:
2 4 0 0 2 1 3 -1 2 -2 4 0 0 2 1 3 -1 2 0

Output:
YES NO

• $1 \le t \le 100$
• $2 \le n \le 1000$
• $-100 \le x,y \le 100$
• $1 \le t \le 100$
• $2 \le n \le 10^6$
• $\sum n \le 10^6$
• $-10^9 \le x,y \le 10^9$