Oil

An oil company drills one well to bring oil up from deposits buried in the earth. A newly found deposit is rarely a single body. It usually splits into many parts that lie in layers.

The company simplifies the situation to a 2-dimensional model. Each deposit is a horizontal segment parallel to the surface, and the well is drilled from the surface along a straight line. The well takes oil from every deposit it touches on the way down, and touching a deposit at an endpoint of its segment still empties that whole deposit. The oil held by a deposit equals the width of the deposit, so the yield of a well is the sum of the widths of the deposits it touches.

The well goes downward from the surface, so it is never horizontal.

Find the largest amount of oil one well can extract.

Figure 1: oil layers buried in the earth. The picture matches the first example input.

The first line contains an integer $n$ ($1 \le n \le 2000$), the number of deposits. Each of the next $n$ lines contains three integers $x_0$, $x_1$, and $y$ describing one deposit: the deposit is the segment whose endpoints are $(x_0, y)$ and $(x_1, y)$, where $y$ is the depth below the surface. The values satisfy $|x_0|, |x_1| \le 10^6$ and $1 \le y \le 10^6$. No two deposits share a point. Note that $x_0$ may be larger than $x_1$, and a deposit with $x_0 = x_1$ has width 0.

Print one integer, the maximum amount of oil that one well can extract.