**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

# Subtask 1 (45 points)

- 1 \le t \le 100
- 2 \le n \le 1000
- -100 \le x,y \le 100

# Subtask 2 (55 points)

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