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 \neq 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 \neq 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.