Alice is playing a game with Bob. She hides an array $A$ of $N$ integers from Bob, and asks him to guess the numbers in it. In a single question, if Bob gives Alice a pair of indices $(i,j)$ with $i\ne j$, Alice does the following actions in order:

1. Define $x:=A_i$ and $y:=A_j$.
2. Set $A_i:=x+y$ and $A_j:=x-y$.
3. Tell Bob the new value of $A_j$.

Alice allows at most $N$ questions from Bob. Can you help him figure out the original array (that is, the array $A$ before Alice performs any operations on it?

Constraints

$2\le N\le {10}^4$

All elements of $A$ are initially integers in the range $[-{10}^9,{10}^9]$.

Subtask 1 [20%]

$N=2$

Subtask 2 [20%]

$N=3$

Subtask 3 [60%]

No additional constraints.

Interaction

This is an interactive problem, where you and the judge exchange information back-and-forth to solve the problem.

At first, you should read in a line containing the integer $N$.

You will then start the interaction by proceeding with your questions. Each question should be formatted as ? i j followed by a \n character, with $1\le i,j\le N$ and $i\ne j$. In response, Alice will perform the three actions described in the statement, giving Bob the value of $A_j$ as an integer on its own line.

If you believe you have the solution, you may output ! followed by a space-separated list of $N$ integers $A_1,A_2,\dots ,A_N$, the original elements of $A$. You must terminate your program immediately after performing this operation. Note that this operation does not count towards the limit of $N$ questions.

Also, Alice does not like very large numbers, so all elements of the array must stay in the range $[-{10}^{18},{10}^{18}]$.

If at any point you attempt an invalid question (such as an invalid output format or a prohibited pair of indices), an element of the array goes out of the range $[-{10}^{18},{10}^{18}]$, or you exceed the limit of $N$ questions, Alice will respond with ${10}^{18}+1$. You should terminate your program immediately after receiving this feedback to receive a Wrong Answer verdict, or you may receive an arbitrary verdict. If the final list you output is incorrect, you will receive a Wrong Answer verdict. Otherwise, you will receive a verdict of Accepted for the corresponding test case.

Please note that you may need to flush stdout after each operation, or interaction may halt. In C++, this can be done with fflush(stdout) or cout << flush (depending on whether you use printf or cout). In Java, this can be done with System.out.flush(). In Python, you can use sys.stdout.flush().

Sample Interaction

>>> denotes your output. Do not print this out.

In this case, $A$ is originally $[2,5,4]$.

3
>>> ? 2 1
3
>>> ? 1 3
-1
>>> ? 2 3
8
>>> ! 2 5 4

Explanation

After the first question, $A$ becomes $[3,7,4]$. Alice responds with the new value of $A_j$, which is $3$.

After the second question, $A$ becomes $[7,7,-1]$. Alice responds with the new value of $A_j$, which is $-1$.

After the third question, $A$ becomes $[7,6,8]$. Alice responds with the new value of $A_j$, which is $8$.

This interaction would receive an Accepted verdict, since it correctly guessed the original list of numbers after asking no more than $N$ questions. Note that the interaction may not represent an optimal or correct strategy to solve the problem, and is only presented for clarity purposes.