line symmetric

You are given a simple polygon in a two-dimensional plane. Please check whether we can move at most one point such that the simple polygon becomes a line-symmetric simple polygon.

Note that you cannot reorder these points. If you move the $i$-th point, it still connects to the $(i-1)$-th point and the $(i+1)$-th point in the original order. Also, you cannot move a point to a location having an existing point.

The first line contains an integer $T$ indicating the number of tests.

Each test begins with one line containing one integer $n$, denoting the number of points in the polygon. Then, the $i$-th line in the following $n$ lines contains two integers $x_i, y_i$, $(x_i, y_i)$ is the coordinate of the $i$-th point. For any $1 \le i < n$, the $i$-th point is connected to the $(i+1)$-th point with an edge. Also, the $n$-th point is connected to the first point.

* $1 \le T \le 40$

* $3 \le n \le 1000$

* coordinates are in the range $[-1000, 1000]$

For each test, if you can move at most one point making the polygon line-symmetric, print a character 'Y' in a line, otherwise print a character 'N' in a line. Please note that the final polygon also has to be a simple polygon.

3
3
1 1
1 2
2 2
4
1 1
1 2
2 2
2 1
7
10 0
5 1
6 2
2 3
2 8
11 7
8 5

Y
Y
N

2019 Multi-University Training Contest 5