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 ii-th point, it still connects to the (i−1)(i−1)-th point and the (i+1)(i+1)-th point in the original order. Also, you cannot move a point to a location having an existing point.
Input
The first line contains an integer TT indicating the number of tests.
Each test begins with one line containing one integer nn, denoting the number of points in the polygon. Then, the ii-th line in the following nn lines contains two integers xi,yixi,yi, (xi,yi)(xi,yi) is the coordinate of the ii-th point. For any 1≤i<n1≤i<n, the ii-th point is connected to the (i+1)(i+1)-th point with an edge. Also, the nn-th point is connected to the first point.
* 1≤T≤401≤T≤40
* 3≤n≤10003≤n≤1000
* coordinates are in the range [−1000,1000]
Output
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.