Your company pays you $0.55 per mile that you drive your own car while you’re delivering pizzas, which is definitely more than you pay for gas. But they’ve installed a GPS system that tracks where you drive, and won’t credit you if you retrace your own steps.

You need to get from point A to point B via the longest possible path, so as to maximize your earnings. Given a set of waypoints, with the distances between them, return the total reimbursement you’ll be requesting if you travel from A to B via the longest path.

You can drive either way between waypoints, and can visit the same waypoint multiple times (including A or B), but you can’t travel along the same path between the same two waypoints twice. There may be multiple paths between the same two waypoints.

Input:
Distances between waypoints, separated by spaces. For example, “A5C C12B” means that the distance from A to C is 5 miles, and from C to B is 12 miles. The distance will always be a positive integer. Waypoint labels are always one letter.

Output:
The dollar amount you’ll be reimbursed if you drive the longest path from waypoint A to waypoint B, formatted to 2 decimal places.