D2. XOR Break — Game Versiontime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThis is an interactive problem.This is the game version of the problem. Note that the solution of this problem may or may not share ideas with the solution of the solo version. You can solve and get points for both versions independently.Alice and Bob are playing a game. The game starts with a positive integer n, with players taking turns. On each turn of the game, the following sequence of events takes place:  The player having the integer p breaks it into two integers p_{1} and p_{2}, where 0 \lt p_{1} \lt p, 0 \lt p_{2} \lt p and p_{1} \oplus p_{2} = p.  If no such p_{1}, p_{2} exist, the player loses.  Otherwise, the opponent does either select the integer p_{1} or p_{2}.  The game continues with the selected integer. The opponent will try to break it. As Alice, your goal is to win. You can execute a maximum of 63 break operations. You have the choice to play first or second. The system will act for Bob.Here \oplus denotes the bitwise XOR operation.InputEach test contains multiple test cases. The first line of input contains a single integer t (1 \leq t \leq 1000) — the number of test cases.The only line of each test case contains a single integer n (1 \leq n \leq 10^{18}) — the number the game starts with.InteractionFor each test case, the interaction begins by reading the integer n.After reading n, print a single line containing either "first" or "second", denoting what you want to play as (as first or second correspondingly).On Alice's turn, you are required to print two positive integers, p_{1} and p_{2} such that 0 \lt p_{1} \lt p, 0 \lt p_{2} \lt p and p_{1} \oplus p_{2} = p. Here, p equals one of the two integers printed by Bob in the previous turn. If no turn has occurred previously, p is equal to n. If Alice cannot perform a break operation, print "0 0" to receive a Wrong answer verdict.On Bob's turn, you should read two integers, p_{1} and p_{2} such that 0 \lt p_{1} \lt p, 0 \lt p_{2} \lt p and p_{1} \oplus p_{2} = p. Here, p equals one of the two integers printed by Alice in the previous turn. If no turn has occurred previously, p is equal to n. If Bob cannot perform a break operation p_{1} = 0 and p_2 = 0 in which case you should proceed to the next test case.If any break operation performed by Alice is invalid, the interactor prints "-1 -1" and your code should promptly exit to receive a wrong answer verdict.If Alice performs 63 turns and Bob can still execute a break operation on the current integers, the interactor prints "-1 -1", and your code should promptly exit to receive a wrong answer verdict.After printing a query, do not forget to output the end of line and flush the output. Otherwise, you will get Idleness limit exceeded. To do this, use:   fflush(stdout) or cout.flush() in C++;  System.out.flush() in Java;  flush(output) in Pascal;  stdout.flush() in Python;  see the documentation for other languages. In this problem, hacks are disabled.ExampleInput
4
1

0 0
3


0 0
13


3 4

0 0
777777770001


0 0Output


second


first
2 1


first
10 7

1 2


first
777777770000 1NoteExplanation for the interaction.Interactor / BobAliceExplanation4t1n for the first test casesecondAlice chooses to go second0 0Bob says he cannot break p = 13n for the second test casefirstAlice chooses to go first1 2Alice breaks p = 3 into p_1 = 1 and p_2 = 20 0Bob says he cannot break p = 1 or p = 213n for the third test casefirstAlice chooses to go first10 7Alice breaks p = 13 into p_1 = 10 and p_2 = 73 4Bob breaks p = 7 into p_1 = 3 and p_2 = 41 2Alice breaks p = 3 into p_1 = 1 and p_2 = 20 0Bob says he cannot break p = 1 or p = 2777777770001n for the fourth test casefirstAlice chooses to go first777777770000 1Alice breaks p = 777\,777\,770\,001 into p_1 = 777\,777\,770\,000 and p_2 = 10 0Bob says he cannot perform break operation.This table is for explanation only and does not reflect the actual behavior of the interactor. Note that in the last test case Bob could choose p_1 and perform a break operation but he gave up.
4
1

0 0
3


0 0
13


3 4

0 0
777777770001


0 0
  second   first 2 1   first 10 7  1 2   first 777777770000 1
['bitmasks', 'games', 'greedy', 'interactive', '*2400']