Problem: This is an interactive problem. You should use flush operation after each printed line. For example, in C++ you should use fflush(stdout), in Java you should use System.out.flush(), and in Pascal — flush(output).

In this problem you should guess an array a which is unknown for you. The only information you have initially is the length n of the array a.

The only allowed action is to ask the sum of two elements by their indices. Formally, you can print two indices i and j (the indices should be distinct). Then your program should read the response: the single integer equals to ai + aj.

It is easy to prove that it is always possible to guess the array using at most n requests.

Write a program that will guess the array a by making at most n requests.

Interaction

In each test your program should guess a single array.

The input starts with a line containing integer n (3 ≤ n ≤ 5000) — the length of the array. Your program should read it at first.

After that your program should print to the standard output the requests about the sum of two elements or inform that the array is guessed.

  * In case your program is making a request to ask the sum of two elements, it should print line in the format "? i j" (i and j are distinct integers between 1 and n), where i and j are indices in the array a.
  * In case your program informs that the array is guessed, it should print line in the format "! a1 a2 ... an" (it is guaranteed that all ai are positive integers not exceeding 105), where ai is the i-th element of the array a. 



The response on a request is a single integer equal to ai + aj, printed on a separate line.

Your program can do at most n requests. Note that the final line «! a1 a2 ... an» is not counted as a request.

Do not forget about flush operation after each printed line.

After you program prints the guessed array, it should terminate normally.

Example

Input

5
 
9
 
7
 
9
 
11
 
6
 

Output

 
? 1 5
 
? 2 3
 
? 4 1
 
? 5 2
 
? 3 4
 
! 4 6 1 5 5

Note

The format of a test to make a hack is:

  * The first line contains an integer number n (3 ≤ n ≤ 5000) — the length of the array.
  * The second line contains n numbers a1, a2, ..., an (1 ≤ ai ≤ 105) — the elements of the array to guess. 

Solution (in JAVA):

Solution:

import java.util.*;
import java.lang.*;
import java.io.*;

public class CO_727C
{
	static int imax=Integer.MAX_VALUE,imin=Integer.MIN_VALUE;
	static long lmax=Long.MAX_VALUE,lmin=Long.MIN_VALUE;
	static long mod=(long)1e9+7;
	public static void main (String[] args) throws java.lang.Exception
	{
		InputReader in =new InputReader(System.in);
		PrintWriter out=new PrintWriter(System.out);
//		int test=in.ni();
 		int test=1;
 		int i=0,j=0;	
		while(test-->0){
			int n=in.ni();
			System.out.println("? 1 2");
			System.out.flush();
			int sum1=in.ni();
			System.out.println("? 2 3");
			System.out.flush();
			int sum2=in.ni();
			System.out.println("? 1 3");
			System.out.flush();
			int sum3=in.ni();
			int arr[]=new int[n];
			arr[0]=(sum1-sum2+sum3)/2;
			arr[2]=sum3-arr[0];
			arr[1]=sum2-arr[2];
			for(i=1;i<=n-3;i++){
				System.out.println("? 1 "+(i+3));
				System.out.flush();
				int tmp=in.ni();
				arr[i+3-1]=tmp-arr[0];
			}
			out.print("!");
			for(int x:arr){
				out.print(" "+x);
			}
			out.println();
		}
	out.close();
	}
	
	static class Pair{
		int x,y;
		Pair(int x,int y){
			this.x=x;
			this.y=y;
		}
		public String toString(){
			return x+" "+y;
		}
	}
	static void print(int arr[],int len){
		for(int i=0;i<len;i++)
		System.out.print(arr[i]+" ");
		System.out.println();
	}
	
	static class InputReader
	{
	 
	    private InputStream stream;
	    private byte[] buf = new byte[1024];
	    private int curChar;
	    private int numChars;
	 
	    public InputReader(InputStream stream) {
	        this.stream = stream;
	    }
	 
	    public int read() {
	        if (numChars == -1)
	            throw new InputMismatchException();
	        if (curChar >= numChars) {
	            curChar = 0;
	            try {
	                numChars = stream.read(buf);
	            } catch (IOException e) {
	                throw new InputMismatchException();
	            }
	            if (numChars <= 0)
	                return -1;
	        }
	        return buf[curChar++];
	    }
	 
	    public int ni() {
	        int c = read();
	        while (isSpaceChar(c))
	            c = read();
	        int sgn = 1;
	        if (c == '-') {
	            sgn = -1;
	            c = read();
	        }
	        int res = 0;
	        do {
	            if (c < '0' || c > '9')
	                throw new InputMismatchException();
	            res *= 10;
	            res += c & 15;
	            c = read();
	        } while (!isSpaceChar(c));
	        return res * sgn;
	    }
	 
	    public long nl() {
	        int c = read();
	        while (isSpaceChar(c))
	            c = read();
	        int sgn = 1;
	        if (c == '-') {
	            sgn = -1;
	            c = read();
	        }
	        long res = 0;
	        do {
	            if (c < '0' || c > '9')
	                throw new InputMismatchException();
	            res *= 10;
	            res += c & 15;
	            c = read();
	        } while (!isSpaceChar(c));
	        return res * sgn;
	    }
	 
	    public String ns() {
	        int c = read();
	        while (isSpaceChar(c))
	            c = read();
	        StringBuilder res = new StringBuilder();
	        do {
	            res.appendCodePoint(c);
	            c = read();
	        } while (!isSpaceChar(c));
	        return res.toString();
	    }
	 
	    public String nLine() {
	        int c = read();
	        //while (c != '\n' && c != '\r' && c != '\t' && c != -1)
	        //c = read();
	        StringBuilder res = new StringBuilder();
	        do {
	            res.appendCodePoint(c);
	            c = read();
	        } while (c != '\n' && c != '\r' && c != '\t' && c != -1);
	        return res.toString();
	    }
	 
	    public static boolean isSpaceChar(int c) {
	        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	    }
	 
	}   

}