Problem C - Robotruck

## Background

This problem is about a robotic truck
that distributes mail packages to several locations in a factory. The robot
sits at the end of a conveyer at the mail office and waits for packages to be
loaded into its cargo area. The robot has a maximum load capacity, which means
that it may have to perform several round trips to complete its task. Provided
that the maximum capacity is not exceeded, the robot can stop the conveyer at
any time and start a round trip distributing the already collected packages.
The packages must be delivered in the incoming order.

The distance of a round trip is computed
in a grid by measuring the number of robot moves from the mail office, at
location (0,0), to the location of delivery of the first package, the number of
moves between package delivery locations, until the last package, and then the
number of moves from the last location back to the mail office. The robot moves
a cell at a time either horizontally or vertically in the factory plant grid.
For example, consider four packages, to be delivered at the locations (1,2),
(1,0), (3,1), and (3,1). By dividing these packages into two round trips of two
packages each, the number of moves in the first trip is 3+2+1=6, and 4+0+4=8 in
the second trip. Notice that the two last packages are delivered at the same
location and thus the number of moves between them is 0.

## Problem

Given a sequence of packages, compute the
minimum distance the robot must travel to deliver all packages.

The input consists of a line containing
one positive integer indicating the maximum capacity of the robot, a line
containing one positive integer **N**, not greater
than 100,000, which is the number of packages to be loaded from the conveyer.
Next, there are **N** lines containing, for each
package, two non-negative integers to indicate its delivery location in the
grid, and a non-negative integer to indicate its weight. The weight of the
packages is always smaller than the robotŐs maximum load capacity. The order of
the input is the order of appearance in the conveyer.

One line containing one integer
representing the minimum number of moves the robot must travel to deliver all
the packages.

## Sample Input

10

4

1 2 3

1 0 3

3 1 4

3 1 4

14