Now You Think with Portals

We are in a skyscraper and want to reach the ~T~-th floor.
We start from the ~S~-th floor and can use ~2~ methods to change floors:

• via ladders: each ladder moves us from the current floor to either the next floor up or the next floor down.
• via portals: each floor provides (up to) ~2~ portals.
  Each portal can take us to a higher floor or a lower floor.
  But which floors? We don't know! The portals are pre-defined, but unknown to us in advance.
  The only thing we know is that:
  • if we use the up portal from the ~i~-th floor, no subsequent portal will take us to the ~i~-th floor or any floor below it, and
  • if we use the down portal, no subsequent portal will take us to the ~i~-th floor or any floor above it. Therefore, a floor might have fewer than ~2~ portals.

For example, if floor ~1~ has a portal to floor ~2~ (up portal), then floor ~2~ cannot have a down portal anywhere.

You need to find the best way to get from floor ~S~ to floor ~T~.

The ideal solution avoids using ladders altogether!

Input (STDIN) - Output (STDOUT)

This problem is interactive, meaning you give instructions to the judge, and it responds with information for you to proceed.

1. The first line contains ~3~ integers ~F~, ~S~, and ~T~: the number of floors, the starting floor, and the floor where the exit is.
   You are initially on floor ~S~.
2. As long as you are not on floor ~T~:
   • You print your move: LADDER UP, LADDER DOWN, PORTAL UP, PORTAL DOWN,
   • The judge prints the floor number ~x~ you land on, in the form OK x, and
   • If you requested a PORTAL move on a floor that doesn't have the corresponding portal, the judge will print SAME.
3. Once you reach floor ~T~, the game ends and the judge computes your score.

Your score for this game is:
~100\% - \frac{\text{number of ladder moves}}{\text{total moves}}~

Example

Input (STDIN)

10 3 7

One possible sequence of moves could be:

This solution would score ~{7 - 3 \over 7} = 57\%~.

Note:

To ensure the interactive grader works properly, you must flush the lines you print.
This is done as follows:

• In Python: print() does this automatically

  print("LADDER UP")
  

• In C/C++ (cstdio): use printf as usual

  printf("LADDER UP\n");
  

• In C++ (iostream): use endl

  cout << "LADDER UP" << endl;