Optimal fly P61365

A fly just travelled between two points in the plane, stopping at several windows (segments) on its way. The fly does not have a very big brain, but it is powerful enough to fly in a straight line between stops. Now the fly wants to go back and visit the windows in reverse order, but it is still worried about efficiency. Is the reverse path optimal? Please help the fly with your bigger brain.

Input

Input consists of several cases, which only have integer numbers. Every case begins with the number of segments n. Follow the description of the s₁ …s_n segments, in the order the fly visits them, each with two pairs (x, y) with the coordinates of its two endpoints. Follow n+2 pairs (x, y) with the coordinates of the points a_i where the fly stopped at the segments, in order. The first pair is the initial position a₀, and the last pair is the final position a_n+1.

Assume 1 ≤ n ≤ 10⁴. Segments are different, and do not intersect. The polygonal line a_n+1 … a₀ does not cross any segment. For all 1 ≤ i ≤ n, a_i is strictly inside the segment ‍s_i. The length of each window and flight segment is strictly positive, and at most 1000. No coordinate is larger than 10⁶ in absolute value.

Output

Print “yes” if the polygonal line a_n+1 … a₀ is the shortest path between a_n+1 and a₀ that visits the segments s_n … s₁ in this order. Print “no” otherwise.

Hint

All the required computations can be made with long longs without overflows.