Problem: This is an interactive problem. You have to use a flush operation right after printing each line. For example, in C++ you should use the function fflush(stdout), in Java — System.out.flush(), in Pascal — flush(output) and in Python — sys.stdout.flush().

Mr. Chanek wants to buy a flamingo to accompany his chickens on his farm. Before going to the pet shop, Mr. Chanek stops at an animal festival to have fun. It turns out there is a carnival game with a flamingo as the prize.

There are N mysterious cages, which are numbered from 1 to N. Cage i has A_i (0 ≤ A_i ≤ 10^3) flamingoes inside (1 ≤ i ≤ N). However, the game master keeps the number of flamingoes inside a secret. To win the flamingo, Mr. Chanek must guess the number of flamingoes in each cage.

Coincidentally, Mr. Chanek has N coins. Each coin can be used to ask once, what is the total number of flamingoes inside cages numbered L to R inclusive? With L < R.

Input

Use standard input to read the responses of your questions.

Initially, the judge will give an integer N (3 ≤ N ≤ 10^3), the number of cages, and the number of coins Mr. Chanek has.

For each of your questions, the jury will give an integer that denotes the number of flamingoes from cage L to R inclusive.

If your program does not guess the flamingoes or ask other questions, you will get "Wrong Answer". Of course, if your program asks more questions than the allowed number, your program will get "Wrong Answer".

Output

To ask questions, your program must use standard output.

Then, you can ask at most N questions. Questions are asked in the format "? L R", (1 ≤ L < R ≤ N). 

To guess the flamingoes, print a line that starts with "!" followed by N integers where the i-th integer denotes the number of flamingo in cage i. After answering, your program must terminate or will receive the "idle limit exceeded" verdict. You can only guess the flamingoes once.

Examples

Input

6
 
5
 
15
 
10
 

Output

 
? 1 2
 
? 5 6
 
? 3 4
 
! 1 4 4 6 7 8

Note

In the sample input, the correct flamingoes amount is [1, 4, 4, 6, 7, 8].

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class Main {
    static PrintWriter pw;
    static Scanner sc;
    static long ceildiv(long x, long y) { return y==0?inf:(x+y-1)/y; }
    static int mod(long x, int m) { return (int)((x%m+m)%m); }
    static void put(TreeMap<Integer, Integer> map, Integer p){if(map.containsKey(p)) map.replace(p, map.get(p)+1); else map.put(p, 1); }
    static void rem(TreeMap<Integer, Integer> map, Integer p){ if(map.get(p)==1) map.remove(p);else map.replace(p, map.get(p)-1); }
    static void printf(double x, int dig){ String s="%."+dig+"f"; pw.printf(s, x); }
    static long gcd(long x, long y) {return y==0?x:gcd(y, x%y);}
    static int Int(boolean x){ return x?1:0; }
    static final int inf=(int)1e9, mod=inf+7;
    static boolean[] visit;
    static final double r2=Math.sqrt(2), eps=1e-12;
    public static void main(String[] args) throws IOException {
        sc = new Scanner(System.in);
        pw=new PrintWriter(System.out);
        int n=sc.nextInt();
        Pair p=new Pair(1, 2);
        int[] ans=new int[n], arr=new int[n-1];
        int i=0;
        while(i<arr.length){
            pw.print("? ");
            pw.println(p);
            pw.flush();
            p.y++;
            int x=sc.nextInt();
            arr[i]=x;
            if(i>0)
                ans[i+1]=x-arr[i-1];
            i++;
        }
        pw.println("? 2 3");
        pw.flush();
        ans[1]=sc.nextInt()-ans[2];
        ans[0]=arr[0]-ans[1];
        pw.print("! ");
        printArr(ans);
        pw.close();
    }
    static class rectangle{
        segment l, r, up, down;
        public rectangle(point lt, point rb){
            point lb=new point(lt.x, rb.y), rt=new point(rb.x, lt.y);
            l=new segment(lt, lb);
            r=new segment(rt, rb);
            up=new segment(lt, rt);
            down=new segment(lb, rb);
        }
        public boolean intersect(segment s){
            return s.intersect(l) || s.intersect(r) || s.intersect(up) || s.intersect(down);
        }
    }
    static boolean inside(segment s, point lt, point rb){
        Pair xs=new Pair((int)lt.x, (int)rb.x), ys=new Pair((int)rb.y, (int)lt.y);
        return inRange((int)s.st.x, xs) && inRange((int)s.end.x, xs) && inRange((int)s.st.y, ys) && inRange((int)s.end.y, ys);
    }
    static boolean inRange(int x, Pair p){
        return x<=p.y && x>=p.x;
    }
    static class point{
        double x, y;
        public point(double a, double b){
            x=a;
            y=b;
        }
        public String toString(){
            return x+" "+y;
        }
    }

    static class segment{
        point st, end;
        boolean p;
        double x, y, c;
        public segment(point st, point end){
            this.st=st;
            this.end=end;
            double dx=end.x-st.x, dy=end.y-st.y;
            double m;
            p=zero(Math.abs(dx)+Math.abs(dy));
            if(Math.abs(dx)<eps)
                m=inf;
            else
                m=dy/dx;
            double b=st.y-(m*st.x);
            if(m==inf){
                x=1;
                y=0;
                c=-st.x;
            }else{
                x=-m;
                y=1;
                c=-b;
            }
        }
        public segment(double a, double b, double z){
            x=a; y=b; c=z;
            if(y==0){
                st=new point(-c, -1e6);
                end=new point(-c, 1e6);
            }else if(zero(x/y)){
                st=new point(-1e6, -c);
                end=new point(1e6, -c);
            }else{
                double m=-x/y;
                if(m>1){
                    st=new point(-1e6, -1e6);
                    end=new point(1e6, 1e6);
                }else{
                    st=new point(-1e6, -1e6*m);
                    end=new point(1e6, 1e6*m);
                }
            }
        }
        public boolean intersect(segment s){
            double m1=s.y==0?inf:s.x/s.y, m2=y==0?inf:x/y;
            if(s.p)
                return inSeg(s.st.x, s.st.y, this);
            else if(p)
                return inSeg(st.x, st.y, s);
            if(Math.abs(m1-m2)<eps)
                return Math.abs(s.c-c)<eps;
            double a,b, r;
            if(!zero(s.x) && !zero(s.y) && !zero(x) && !zero(y)){
                r=(s.y/y);
                a=(c*r-s.c)/(s.x-x*r);
                r=s.x/x;
                b=(c*r-s.c)/(s.y-y*r);
            }else{
                if(!zero(s.y) && !zero(y)){
                    r=(s.y/y);
                    a=(c*r-s.c)/(s.x-x*r);
                    b=zero(s.x)?-s.c/s.y:-c/y;
                }else if(!zero(s.x) && !zero(x)){
                    r=s.x/x;
                    b=(c*r-s.c)/(s.y-y*r);
                    a=zero(s.y)?-s.c/s.x:-c/x;
                }else{
                    if(y==0){
                        a=-c/x;
                        b=-s.c/s.y;
                    }else{
                        a=-s.c/s.x;
                        b=-c/y;
                    }
                }
            }
            return inSeg(a, b, this) && inSeg(a, b, s);
        }
        public String toString(){
            return x+" "+y+" "+c;
        }
        public boolean zero(double x){
            return Math.abs(x)<eps;
        }
        public boolean inSeg(double x, double y, segment s){
            return validX(x, s) && validY(y, s);
        }
        public boolean validX(double x, segment s){
            if(Math.abs(x-s.st.x)<eps || Math.abs(x-s.end.x)<eps)
                return true;
            return x>Math.min(s.st.x, s.end.x) && x<Math.max(s.st.x, s.end.x);
        }
        public boolean validY(double y, segment s){
            if(Math.abs(y-s.st.y)<eps || Math.abs(y-s.end.y)<eps)
                return true;
            return y>Math.min(s.st.y, s.end.y) && y<Math.max(s.st.y, s.end.y);
        }
    }
    static void printArr(int[] arr) {
        for (int i = 0; i < arr.length - 1; i++)
            pw.print(arr[i] + " ");
        pw.println(arr[arr.length - 1]);
    }
    static void printArr(long[] arr) {
        for (int i = 0; i < arr.length - 1; i++)
            pw.print(arr[i] + " ");
        pw.println(arr[arr.length - 1]);
    }
    static void printArr(Integer[] arr) {
        for (int i = 0; i < arr.length; i++)
            pw.print(arr[i] + " ");
        pw.println();
    }
    static void printArr(char[] arr) {
        for (int i = 0; i < arr.length; i++)
            pw.print(arr[i]==0? '1': arr[i]);
        pw.println();
    }
    static void printArr(ArrayList<Integer> list) {
        for (int i = 0; i < list.size(); i++)
            pw.print(list.get(i)+" ");
        pw.println();
    }
    static class Scanner {
        StringTokenizer st;
        BufferedReader br;
        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public Scanner(FileReader r) {
            br = new BufferedReader(r);
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

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

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

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }
        public int[] nextDigits() throws IOException{
            String s=nextLine();
            int[] arr=new int[s.length()];
            for(int i=0; i<arr.length; i++)
                arr[i]=s.charAt(i)-'0';
            return arr;
        }
        public int[] nextArr(int n) throws IOException {
            int[] arr = new int[n];
            for (int i = 0; i < arr.length; i++)
                arr[i] = nextInt();
            return arr;
        }
        public Integer[] nextsort(int n) throws IOException{
            Integer[] arr=new Integer[n];
            for(int i=0; i<n; i++)
                arr[i]=nextInt();
            return arr;
        }
        public Pair nextPair() throws IOException{
            return new Pair(nextInt(), nextInt());
        }
        public Pair[] nextPairArr(int n) throws IOException{
            Pair[] arr=new Pair[n];
            for(int i=0; i<n; i++)
                arr[i]=nextPair();
            return arr;
        }
        public boolean ready() throws IOException {
            return br.ready();
        }
    }
    static class Pair implements Comparable<Pair>{
        int x;
        int y;
        public Pair(int x, int y) {
            this.x=x;
            this.y=y;
        }
        public int hashCode() {
            return (this.x*1000+this.y);
        }
        public int compareTo(Pair p){
            return x-p.x;
        }
        public boolean equals(Object obj) {
            if (obj == null) {
                return false;
            }
            if (this.getClass() != obj.getClass()) {
                return false;
            }
            Pair p = (Pair) obj;
            return this.x==p.x && this.y==p.y;
        }
        public Pair clone(){
            return new Pair(x, y);
        }
        public String toString(){
            return this.x+" "+this.y;
        }
        public void add(Pair p){
            x+=p.x;
            y+=p.y;
        }
    }
    static class Union{
        int[] rep, size;
        int sets;
        public Union(int n){
            rep=new int[n];
            size=new int[n];
            sets=n;
            for(int i=0; i<n; i++){
                rep[i]=i;
                size[i]=1;
            }
        }
        public void join(int x, int y){
            int a=getSet(x), b=getSet(y);
            if(a==b){
                return;
            }
            sets--;
            if(size[a]>size[b]){
                rep[b]=a;
                size[a]+=size[b];
            }else{
                rep[a]=b;
                size[b]+=size[a];
            }
        }
        public int getSet(int x){
            if(rep[x]==x)
                return x;
            return rep[x]=getSet(rep[x]);
        }
    }
}