This is an interactive problem
The Zoldyck mansion is enormous, with dozens of rooms and hundreds of illuminating sources — light bulbs, chandeliers, lamps, etc.
You are recently hired by the Zoldyck family as a butler. Your daily job involves sitting in the illumination control room and control all the illuminating sources in the mansion.
In the control room, there are $n$ switches. Each switch controls exactly one illuminating source. Switches and illuminating sources are numbered from $1$ to $n$, inclusive. However, there is no documentation, so you do not know which switch controls which illuminating source.
Thus, your only choice is to repeat the following operation:
Toggle some of the switches (at least one).
Go around the entire mansion, check all the state of all $n$ illuminating sources.
As the mansion is enormous, you want to go around it at most $32$ times.
First your program reads the integer $n$ $(1 \le n \le 1\, 000)$.
Then the following process repeats:
Your program writes to the standard output one of the following:
ASK $k \; a_1 \; a_2 \; \ldots \; a_ k$ ($1 \le k \le n, 1 \le a_ i \le n$ and all $a_ i$ are unique) — you toggle $k$ switches $a_1, a_2, \ldots , a_ k$, and want to know what are the $k$ illuminating sources which are toggled.
ANSWER $b_1 \; b_2 \; \ldots \; b_ n$ $(1 \le b_ i \le n)$ — you want to answer that the illuminating source $i$ is controlled by the switch $b_ i$.
If your program asks a query, $k$ integers will be available in the standard input, representing the illuminating sources which were toggled, in any order. Your program should then read them.
If your program prints an answer, it should then terminate. You are allowed to print an answer exactly once.
Note that you are allowed to interact at most $32 + 1 = 33$ times, $32$ interactions for asking queries and $1$ interaction for answering.
After printing a query do not forget to output end of line and flush the output. Otherwise, your submission may be rejected. To do this, use:
fflush(stdout) or cout.flush() in C++;
System.out.flush() in Java;
stdout.flush() in Python.
|Read||Sample Interaction 1||Write|
ASK 1 1
ASK 2 1 2
ASK 3 1 2 3
1 3 4
ASK 4 1 2 3 4
1 2 3 4
ASK 5 1 2 3 4 5
1 2 3 4 5
ANSWER 1 4 2 3 5