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

public class C {
	public static void solve(FastReader in,PrintWriter out,int nTestCase) {
		int n = in.nextInt();
		int N = n-(n%2==1?0:1);
		int[] temp = new int[n];
		long sum = 0;
		for(int i=1;i<=N;i++) {
			out.println("? "+(i)+" "+((i+1)>N?1:(i+1)));
			out.flush();
			int next = in.nextInt();
			sum += next;
			temp[i-1] = next;
		}
		long t = sum/2;
		for(int i=0;i<N-1;i+=2) {
			t -= temp[i];
		}
		int[] ans = new int[n];
		ans[N-1] = (int)(t);
		for(int i=N-2;i>=0;i--) {
			ans[i] = temp[i]-ans[i+1];
		}
		if(n%2==0) {
			out.println("? "+(N)+" "+(N+1));
			out.flush();
			ans[n-1] = in.nextInt()-ans[n-2];
		}
		out.print("! ");
		for(int i:ans) out.print(i+" ");
//		out.println(ans);
	}
	public static void main(String[] args) {
		FastReader in = new FastReader();
		PrintWriter out = new PrintWriter(System.out);
		int T = 1;
		for(int tt=1;tt<=T;tt++) {
			solve(in,out,tt);
		}
		out.close();
	}
	public static int findSqRt(int n) {
		int i = 1;
		while(i*i<n) i++;
		return i;
	}
	static final Random random=new Random();
	//	static void ruffleSort(Pair[] a) {
	//		int n=a.length;//shuffle, then sort 
	//		for (int i=0; i<n; i++) {
	//			int oi=random.nextInt(n);
	//			Pair temp=a[oi];
	//			a[oi]=a[i]; a[i]=temp;
	//		}
	//		Arrays.sort(a);
	//	}
	static void ruffleSort(int[] a) {
		int n=a.length;//shuffle, then sort 
		for (int i=0; i<n; i++) {
			int oi=random.nextInt(n), temp=a[oi];
			a[oi]=a[i]; a[i]=temp;
		}
		Arrays.sort(a);
	}
	static void fastSort(char[] a) {
		int n=a.length;//shuffle, then sort 
		for (int i=0; i<n; i++) {
			int oi=random.nextInt(n);
			char temp=a[oi];
			a[oi]=a[i]; a[i]=temp;
		}
		Arrays.sort(a);
	}
	static class FastReader 
	{ 
		BufferedReader br; 
		StringTokenizer st; 

		public FastReader() 
		{ 
			br = new BufferedReader(new
					InputStreamReader(System.in)); 
		} 

		String next() 
		{ 
			while (st == null || !st.hasMoreElements()) 
			{ 
				try
				{ 
					st = new StringTokenizer(br.readLine()); 
				} 
				catch (IOException  e) 
				{ 
					e.printStackTrace(); 
				} 
			} 
			return st.nextToken(); 
		} 

		int nextInt() 
		{ 
			return Integer.parseInt(next()); 
		} 

		long nextLong() 
		{ 
			return Long.parseLong(next()); 
		} 

		double nextDouble() 
		{ 
			return Double.parseDouble(next()); 
		} 

		String nextLine() 
		{ 
			String str = ""; 
			try
			{ 
				str = br.readLine(); 
			} 
			catch (IOException e) 
			{ 
				e.printStackTrace(); 
			} 
			return str; 
		} 

		int[] nextArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
	}
}

//class Pair implements Comparable<Pair>{
//    int a;
//    int b;
//    public Pair(int a, int b) {
//        this.a = a;
//        this.b = b;
//    }
//    public int compareTo(Pair o) {
//        if(this.a==o.a)
//            return this.b - o.b;
//        return this.a - o.a;
//    }   
//}