There is a hidden permutation $a_1, a_2,\dots, a_n$ of integers $1, 2,\dots, n$. Your task is to find this permutation.

To do this, you can ask questions: you can choose a binary string $b_1b_2\dots b_n$ and you will receive the binary string $b_{a_1}b_{a_2}\dots b_{a_n}$.

Interaction

This is an interactive problem. Your code will interact with the grader using standard input and output. You should start by reading a single integer $n$: the length of the permutation.

On your turn, you can print one of the following:

• "$?\ b_1b_2\dots b_n$", where $b_i\in\{0, 1\}$: The grader will return the binary string $b_{a_1}b_{a_2}\dots b_{a_n}$.
• "$!\ a_1\ a_2 \dots a_n$": report that the hidden permutation is $a_1, a_2,\dots, a_n$. Your program must terminate after this.

Each line should be followed by a line break. You must make sure the output gets flushed after printing each line.

Constraints

• $1 \le n \le 1000$
• you can ask at most $10$ questions of type $?$

Example

3
? 100
100
? 010
001
? 001
010
! 1 3 2

Explanation: The hidden permutation is $[1, 3, 2]$. In the first question $b_1b_2b_3 = 100$ and the grader returns $b_{a_1}b_{a_2}b_{a_3} = b_1b_3b_2 = 100$. In the second question $b_1b_2b_3 = 010$ and the grader returns $b_1b_3b_2 = 001$.