Cake#2357
Winnie the Pooh, Rabbit, and Piglet came to visit Christopher Robin on his birthday. The main gift was a huge round honey cake with four candles. However, before they could eat the cake, it first needed to be cut into four pieces. Knowing how much Winnie the Pooh loves honey, it could be expected that he would immediately take the largest piece of the cake for himself, and would probably get stuck in the doorway, just as happened when he and Piglet went to visit Rabbit.
To avoid this, Christopher Robin decided to cut the cake into four identical parts. Moreover, to emphasize the importance of the event—since this is not just any cake, but a festive one—and to avoid complicating the process, the cake needs to be cut with two perpendicular cuts passing through its center. Each resulting piece must have exactly one candle. Furthermore, so that no one receives a partial candle and no one is upset, Christopher Robin wants the cuts not to pass through any candle.
The center of the cake is considered the origin of the coordinate system. The first line contains the integer radius (1 \le r \le 10^9) of the cake. The next four lines contain the coordinates of the candles x_i, y_i. It is guaranteed that all the candles are strictly inside the cake.
Print YES if Christopher Robin can cut the cake the way he wants, and NO if he cannot.
Example 1