Some WSA agents travel frequently on official business, and they figured out how to cheat the WSA's working time accounting system. The trick is that if they have to visit a lot of distant cities, they travel more to the east than to the west, and they use local time zones for logging their time. As long as they don't travel around the globe twice, and they choose a reasonably short path, no one would notice.
At least, so they thought. WSA management eventually discovered the cheating (...no they didn't; rather, someone snitched), and they want to estimate the losses. They handed you 10 lists of cities that agents usually visit (with coordinates).
Find the shortest tour visiting all the listed locations without ever traveling West (longitude shall never decrease, except when crossing the antimeridian) and without traveling around the planet more than twice.
The first line contains N, the number of locations and the following N lines are the (latitude, longitude) coordinates of the locations in degrees. (-90 ≤ latitude ≤ 90 increasing to the North and -180 ≤ longitude ≤ 180 increasing to the East and there are no locations exactly at the same longitude or at the poles)
The first line should contain the length of the optimal tour in km (to one meter precision; Earth is approximated as a perfect sphere with R = 6371 km radius).
The second line should contain N+1 numbers separated by whitespace: the indices of the locations in the order they are visited in the optimal tour (indexing starts from 0, based on the order in the input, the last location must be the same as the first one and the longitude of consecutive locations must not decrease more than twice).
6 40 0.5 -60 50 -10 -80 80 1e2 30 -160 -70 140
53904.473044 4 1 5 2 0 3 4