Lie to me#2856
— Nothing personal, but I don't really trust your way of cutting the cake. — That's too bad. — Then prove it. — I'm not that great, but my laptop never lies to me. — I don't see a backpack on you. — Oh no, did I forget to take it?.. Just kidding, of course I did.
Recall that the cake-cutting plan includes the following information: The cake is a regular -gon centered at with one of its vertices at . The entire cake is cut into N+1 pieces, each of which is a convex polygon.
Check that all the pieces are convex polygons, with no three points on a straight line, with vertices given in counterclockwise order. Check that all the pieces have equal area. Check that all the pieces have equal length of their outer boundary—that is, the part of the boundary that follows the original cake's boundary. Also check that all the pieces together form the whole cake.
The first line contains the number (3 \le N \le 100): the number of vertices of the cake. Then the descriptions of N+1 pieces follow. The description of each piece begins with a number K_i (3 \le K_i \le 100)—the number of vertices of the piece. The next K_i lines each contain two coordinates x_i and y_i (-100 \le x_i, y_i \le 100), which represent the vertices of the piece (the order of the points is arbitrary). All coordinates are real numbers given with up to decimal places.
Print "Yes" if the description matches a correct cake cutting, otherwise print "No". It is guaranteed that if the answer is "No", the parameters justifying this answer differ by at least 10^{-6}.
Example 1