Gift
On August 14, the world celebrates two special occasions: the International Team Programming Olympiad among parallels A, A', and B, and the World Girls' Day at LKS. To mark this day, the senior students decided to gift their fellow campmates with unlimited Wi-Fi access in each house. The houses at LKS are rectangular, with sides parallel to the coordinate axes, and they do not intersect the 0x axis.
After successful negotiations with the local provider, the students secured several routers and receivers. However, the provider stipulated that routers must remain near the nearest road, which coincidentally aligns with the line y = 0. Each router must be connected to its neighbors along this line with a cable, and to minimize interference, all cables must be no longer than dh.
One router receives internet from the provider and relays it via cable to other routers. Each router broadcasts wireless internet within a radius of dv. For a house to have internet access, a receiver must be placed at a point within the broadcast radius of at least one router. A single router can transmit signals to multiple receivers.
The senior students have limited funds remaining, having spent most on cola and cookies. Therefore, they aim to minimize the number of routers rented (receivers are provided free of charge). Help them determine the minimum number of routers needed.
Input
The first line contains three numbers: 1 ≤ N ≤ 100000 - the number of houses, and 1 ≤ dv, dh ≤ 100000 - the router's broadcast radius and the maximum cable length. The next N lines describe the coordinates of the houses, each as a quadruple of numbers x_1, y_1, x_2, y_2, where x_1 < x_2 and y_1 < y_2. The coordinates do not exceed 100000 in absolute value. All numbers in the input are integers.
Output
Output the minimum number of routers needed, or -1 if no solution is possible.