Serve the Floors in LOOK Order

An elevator runs the LOOK algorithm. Given the floor it's on, the direction it's heading (UP, DOWN or IDLE) and the floors that have been requested, print the order it stops at them and how many floors it travels.

• Each requested floor is a stop once, however many times it was requested.
• A request for the current floor is served first, without moving.
• Heading UP: stop at every requested floor above, lowest first; then turn and stop at the ones below, highest first. DOWN is the mirror image.
• IDLE: head toward the nearest requested floor (a tie goes UP), then continue as above.

Implement List<Integer> stopOrder(int current, String direction, int[] requests) and long travel(int current, List<Integer> stops).

In Python: stop_order(current, direction, requests) returns a list and travel(current, stops) an int. Python has no TreeSet: sort the distinct floors and split them with bisect. The first line of output is the stops separated by spaces (NONE if there are none), the second the floors traveled.

Input: the current floor and the direction; the number of requests k; then the k requested floors.

Example

Input:
5 UP
5
2 8 5 9 3

Output:
5 8 9 3 2
11

Floor 5 is served where the car stands. Heading up, it stops at 8 and 9, then turns and stops at 3 and 2: 0 + 3 + 1 + 6 + 1 = 11 floors.

• 0 <= floor <= 2 * 10^9 for the current and every requested floor
• 0 <= k <= 2 * 10^5
• the total travel can exceed the range of an int