Donut-shaped Enclosure

The distance system usually used in the two-dimensional plane is Euclidean distance. In Euclidean distance, the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is written as $\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$.

This problem deals with Chebyshev distance instead of Euclidean distance. In Chebyshev distance, the distance between $(x_1, y_1)$ and $(x_2, y_2)$ is written as $\max{(|x_1 - x_2|, |y_1 - y_2|)}$.

For a given distance system, a circle of radius $r$ is the set of points $(x,y)$ whose distance to a specific point $(x_c, y_c)$ is $r$. The shape of a circle depends on which distance system is used. As (Figure 1) shows, under Euclidean distance it is the circular shape we usually know, and under Chebyshev distance a square with side length $2r$ becomes the circle.

Figure 1 : Circles under Euclidean distance and Chebyshev distance

Also, for a given distance system, a donut with inner radius $l$ and outer radius $r$ is the set of points $(x,y)$ whose distance to a specific point $(x_c, y_c)$ is at least $l$ and at most $r$.

In (Figure 2), the left side is a donut under Euclidean distance and the right side is a donut under Chebyshev distance. The gray region is the region included in the donut.

Figure 2 : Donuts under Euclidean distance and Chebyshev distance

Bumsoo is playing with $N$ points $P_1$, $P_2$, $\cdots$, $P_N$ and a donut under Chebyshev distance whose inner radius is $L$ and outer radius is $R$. $P_i$ is located at $(x_i, y_i)$, and Bumsoo can freely change the position of the donut's center as long as he keeps the center's coordinates on a lattice point. If $P_i$ lies in the donut region, Bumsoo is forced to gain $S_i$ points, and if it does not lie in the donut region, he gains no points. Write a program that finds the maximum score Bumsoo can gain.

The first line of the input gives three integers $N$, $L$, $R$ ($1 ≤ N ≤ 10^5$, $1 ≤ L ≤ R ≤ 10^9$), separated by a single space.

The $i$-th of the following $N$ lines gives $x_i$, $y_i$, $S_i$ ($-10^9 ≤ x_i, y_i ≤ 10^9$, $-10^4 ≤ S_i ≤ 10^4$), separated by a single space. Multiple points may be at the same position.

On the first line, print the maximum score Bumsoo can gain.

For the first sample, it is enough to put the donut's center at $(1,0)$ or $(-1,0)$.

For the second sample, the donut has become too large, so the best choice is to include one of the $1$s while avoiding the $-100$s.