A game called Memory is played using ~50~ cards. Each card has one of the letters from A to Y (ASCII 65 to 89) printed on the face, so that each letter appears on exactly two cards. The cards are shuffled into some random order and dealt face down on the table.

Jack plays the game by turning two cards face up so the letters are visible. For each of the ~25~ letters Jack gets a candy from his mother the first time he sees both copies of the letter on the two face up cards. For example, the first time Jack turns over both cards that contain the letter M, he gets a candy. Regardless of whether the letters were equal or not, Jack then turns both cards face down again. The process is repeated until Jack receives ~25~ candies — one for each letter.

You are to implement a procedure play that plays the game. Your implementation should call the procedure faceup(C) which is implemented by the grader. ~C~ is a number between ~1~ and ~50~ denoting a particular card you wish to be turned face up. The card must not currently be face up. faceup(C) returns the character that is printed on the card ~C~.

After every second call to faceup, the grader automatically turns both cards face down again.

Your procedure play may only terminate once Jack has received all ~25~ candies. It is allowed to make calls to faceup(C) even after the moment when Jack gets the last candy.

Example

The following is one possible sequence of calls your procedure play could make, with explanations.

Call	Returned value	Explanation
faceup(~1~)	B	Card ~1~ contains B.
faceup(~7~)	X	Card ~7~ contains X. The letters are not equal.
The grader automatically turns cards 1 and 7 face down.
faceup(~7~)	X	Card ~7~ contains X.
faceup(~15~)	O	Card ~15~ contains O. The letters are not equal.
The grader automatically turns cards 7 and 15 face down.
faceup(~50~)	X	Card ~50~ contains X.
faceup(~7~)	X	Card ~7~ contains X. Jack gets his first candy.
The grader automatically turns cards 50 and 7 face down.
faceup(~7~)	X	Card ~7~ contains X.
faceup(~50~)	X	Card ~50~ contains X. Equal letters, but Jack gets no candy.
The grader automatically turns cards 7 and 50 face down.
faceup(~2~)	B	Card ~2~ contains B.
...
(some function calls were omitted)
...
faceup(~1~)	B	Card ~1~ contains B.
faceup(~2~)	B	Card ~2~ contains B. Jack gets his ~25^{th}~ candy.

Subtask 1 [50 points]

Implement any strategy that obeys the rules of the game and finishes it within the time limit.

For example, there is a simple strategy that always makes exactly ~2 \times (49+48+\dots+2+1) = 2450~ calls to faceup(C).

Subtask 2 [50 points]

Implement a strategy that finishes any possible game with at most ~100~ calls to faceup(C).

Implementation Details

• Implementation folder: /home/ioi2010-contestant/memory/ (prototype: memory.zip)
• To be implemented by contestant: memory.c or memory.cpp or memory.pas
• Contestant interface: memory.h or memory.pas
• Grader interface: grader.h or graderlib.pas
• Sample grader: grader.c or grader.cpp or grader.pas and graderlib.pas
• Sample grader input: grader.in.1.
  Note: the input file contains one line with ~50~ characters denoting the letters on the cards, in order, from ~1~ to ~50~.
• Expected output for sample grader input: if your implementation is correct, the output file will contain OK n where ~n~ is the number of calls to faceup(C).