Problem Statement

This is an interactive problem (a problem in which your program and the judge system communicate through input and output).

The judge holds a hidden positive integer $X$ that has $N$ digits in base $10$.

Find $X$ by asking the following question at most $N$ times.

However, if, after asking at most $N$ questions, you find that $X$ cannot be determined as exactly $1$ possibility no matter how at most $N$ questions are asked, report that instead.

• Specify $2$ different digits in the base-$10$ representation of $X$ and ask for their product.

Constraints

• $2 \leq N \leq 51$
• $X$ is a positive integer that has $N$ digits in base $10$, without leading zeros

Input and Output

$N$

Next, ask at least $0$ and at most $N$ questions in the following format.

• When asking the judge a question

To ask for the product of the $10^a$'s digit and the $10^b$'s digit, print to standard output in the following format. Here, $a,b$ must have no leading zeros and must satisfy $0 \leq a < b \leq N-1$.

$?\ a\  b$

The judge's response is given from standard input in the following format.

$p$

Here, $p$ is the product of the $10^a$'s digit and the $10^b$'s digit of $X$.

However, if you print output in an invalid format during the interaction, or if the number of questions exceeds $N$, then $p = -1$.

In this case, the judge program has already terminated and your submission has been judged as incorrect, so stop your program immediately. Otherwise, the judge result is undefined.

• When answering the problem

When you have finished asking questions, print the integer $X$ you deduced in the following format.

$!\ X$

However, if you find that the integer $X$ cannot be determined as exactly $1$ possibility within $N$ questions, print the following.

$!$ $-1$

1. If the hidden integer $X$ is one that cannot be determined as exactly $1$ possibility within $N$ questions

Your answer is correct only if you correctly report that it cannot be determined; otherwise it is incorrect. Even if you happen to guess the correct value, your answer is incorrect unless you report that it cannot be determined as exactly $1$ possibility.

2. If the hidden integer $X$ is one that can be determined as exactly $1$ possibility within $N$ questions

If you report that it cannot be determined, your answer is incorrect. Otherwise, your answer is correct if the value you deduced and printed equals the integer $X$, and incorrect if it differs.