Signal 1

There are $N$ signals on the coordinate plane. Signal $i$ sits at $(x_i, y_i)$, and no two signals share a position.

A communication system is built by choosing some of the signals and joining them with segments in order of increasing $x$ coordinate. The chosen signals must have pairwise different $x$ coordinates. The length of the system is the sum of the Euclidean distances between consecutive signals, and a system built from a single signal has length 0.

Build the communication system of greatest length so that a signal reaches as far as possible, then report that length.

The first line contains the number of signals $N$ ($1 \le N \le 1000$).

Each of the next $N$ lines contains the coordinates $x_i$ and $y_i$ of one signal, separated by a space ($-10^4 \le x_i, y_i \le 10^4$, and $x_i$ and $y_i$ are integers).

No coordinate pair is given twice.

Print the length of the longest communication system on one line, rounded to six digits after the decimal point. Pad with zeros so that six digits always appear.