This is an interactive problem.

Given a positive integer $n$, the grader generates an unknown 01 sequence $a_1,a_2,\dots,a_n$ of length $n$. You may ask the grader at most $17$ queries to determine the number of 1s in this 01 sequence, i.e., $\sum\limits_{i=1}^n a_i$. It is guaranteed that there is at least one 1.

For each query, you may choose several positions $i_1,i_2,\dots,i_k$. Let $I=\{i_1,i_2,\dots,i_k\}$. The grader will return the value of $(\sum\limits_{j\in I} a_j) \cdot (\sum\limits_{j\notin I} a_j)$.

Input

The first line contains a positive integer $n$ $(1\le n\le 10^5)$, the length of the 01 sequence.

Interaction

For a query, output a line in the following format (without quotes):

? k i_1 i_2 ... i_k $(1\le k\le n,1\le i_1< i_2< \dots< i_k\le n)$.

To output the answer, output a line in the following format (without quotes):

! s, where $s=\sum\limits_{i=1}^n a_i$.

Outputting the answer does not count toward the number of queries.

The interactor is non-adaptive, meaning the answer is fixed before any queries are made and does not depend on the queries you make.

After outputting each query, do not forget to output a newline and flush the output buffer.

You can use the following statements to flush the buffer:

• For C/C++: fflush(stdout)
• For C++: std::cout << std::flush
• For Java: System.out.flush()
• For Python: sys.stdout.flush()

Examples

Input 1

3

2

Output 1

? 2 1 3

! 3

Input 2

3

0

0

Output 2

? 1 1

? 1 2

! 1

Note

The hidden sequence in the first sample is $[1,1,1]$, and the hidden sequence in the second sample is $[0,1,0]$.