Game

Problem Description

Notice：Don't output extra spaces at the end of one line. Dodo bird and ddd are playing a stone game on a 2-d plane. There are $n$ points on the plane where they can put the stone. The rule is as follows:

• Before the game start, The stone is at the first point.
• Dodo and ddd move the stone in turn, Dodo moves first.
• In the first move, the player can move the stone to any point except the first point.
• Starting from the second move, assume the stone is currently at point $x$, and the distance of the stone traveled in the last move is $d$. The player can move the stone to a point $y$ if and only if $\text{distance(x,y)} > d$ and point $y$ has never been visited before.
• If a player cannot make a move, he loses the game. Please determine who will win the game if both player use the best strategy.

Input

The first line contains an integer $T(1 \leq T \leq 100)$, indicating the number of test cases. Each test case contains several lines. The first line contains an integer $n(2 \leq n \leq 2000)$, indicating the number of points. Next $n$ lines, each line contains two integers $x_i, y_i(-10^9 \leq x, y \leq 10^9)$, indicating the coordinate of the i-th point. It is guaranteed that there are at most 12 test cases with $n > 500$.

Output

For each test case, If Dodo can win the game, print "YES". Otherwise, print "NO".

Sample Input

2
5
1 1
0 0
2 0
0 2
2 2
4
1 1
0 0
0 2
2 2

Sample Output

NO
YES

Source

2020 Multi-University Training Contest 7