Lie to me
— Nothing personal, but I don't believe in your ways of cutting the cake. — You'd better believed. — Than prove it. — I'm not so cool, but my notebook never lies to me. — I can't see a backpack on you. — Damn it, haven't I taken it?.. Joke, surely I have.
Reminding that the cake cutting plan contains the following information: The cake is represented as regular N-gon with center at point (0, 0) and one of the vertices at point (1, 0). Whole cake is cut into N+1 pieces. Each of those pieces is convex polygons.
Check if all the pieces are convex polygons without three vertices on one line, in counterclockwise pass order. Check if all the pieces have equal square. Check if all the pieces have equal length of the outer border, i.e. the part of the border that reproduces the initial cake border. Check if is possible to join all the pieces together, so they will form the full cake.
Input
In the fi rst line is given number N (3 ≤ N ≤ 100) — number of the cake vertices. Then the description of N+1 pieces is given. The description of one piece is started with number K_i (3 ≤ K_i ≤ 100) — number of the vertices in the piece. Next K_i number of the vertices in the piece. Next lines contain those vertices listed in random order, given by two coordinates x_i and y_i (-100 ≤ x_i, y_i ≤ 100). Àll the coordiantes are real numbers with not more than 15 decimal places.
Output
Print "Yes", in case the description matches the correct cake cutting, otherwise — "No". It's guaranteed that in case the answer is"No" parameters which provide this answer are not less than 10^{-6}.