6948.Permuted Binary Strings

Time Limit: 1s Memory Limit: 512MB

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.

Input Format(From the terminal/stdin)

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

Output Format(To the terminal/stdout)

Sample Input

Copy 
3
? 100
100
? 010
001
? 001
010
! 1 3 2
 \n
 ·   \n
   \n
 ·   \n
   \n
 ·   \n
   \n
 · · · \n

Sample Output special judge

The hidden permutation is $[1, 3, 2]$ . In the first question $b_1b_2b3 = 100$ and the grader returns $b{a1}b{a2}b{a_3} = b_1b_3b_2 = 100$ . In the second question $b_1b_2b_3 = 010$ and the grader returns $b_1b_3b_2 = 001$ .

Source: CSES, Interactive Problems, 3228

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