Problem: This is an interactive problem.

Little Dormi was faced with an awkward problem at the carnival: he has to guess the edges of an unweighted tree of n nodes! The nodes of the tree are numbered from 1 to n.

The game master only allows him to ask one type of question:

  * Little Dormi picks a node r (1 ≤ r ≤ n), and the game master will reply with an array d_1, d_2, …, d_n, where d_i is the length of the shortest path from node r to i, for all 1 ≤ i ≤ n.



Additionally, to make the game unfair challenge Little Dormi the game master will allow at most ⌈n/2⌉ questions, where ⌈ x ⌉ denotes the smallest integer greater than or equal to x.

Faced with the stomach-churning possibility of not being able to guess the tree, Little Dormi needs your help to devise a winning strategy!

Note that the game master creates the tree before the game starts, and does not change it during the game.

Input

The first line of input contains the integer n (2 ≤ n ≤ 2 000), the number of nodes in the tree.

You will then begin interaction.

Output

When your program has found the tree, first output a line consisting of a single "!" followed by n-1 lines each with two space separated integers a and b, denoting an edge connecting nodes a and b (1 ≤ a, b ≤ n). Once you are done, terminate your program normally immediately after flushing the output stream.

You may output the edges in any order and an edge (a,b) is considered the same as an edge (b,a). Answering is not considered as a query.

Interaction

After taking input, you may make at most ⌈n/2⌉ queries. Each query is made in the format "? r", where r is an integer 1 ≤ r ≤ n that denotes the node you want to pick for that query.

You will then receive n space separated integers d_1, d_2, …, d_n, where d_i is the length of the shortest path from node r to i, followed by a newline.

After printing a query do not forget to output end of line and flush the output. Otherwise, you will get Idleness limit exceeded. To do this, use:

  * fflush(stdout) or cout.flush() in C++; 
  * System.out.flush() in Java; 
  * flush(output) in Pascal; 
  * stdout.flush() in Python; 
  * see documentation for other languages. 



If at any point you make an invalid query or try to make more than ⌈ n/2 ⌉ queries, the interaction will terminate immediately and you will receive a Wrong Answer verdict.

Hacks

To hack a solution, use the following format.

The first line contains the integer n (2 ≤ n ≤ 2 000).

The next n−1 lines contain two integers u and v (1 ≤ u,v ≤ n) denoting an edge between u and v (u ≠ v). These n-1 edges must form a tree.

Examples

Input


4

0 1 2 2

1 0 1 1

Output


? 1

? 2

!
4 2
1 2
2 3


Input


5

2 2 1 1 0


Output


? 5

!
4 5
3 5
2 4
1 3

Note

Here is the tree from the first example.

<image>

Notice that the edges can be output in any order.

Additionally, here are the answers for querying every single node in example 1:

  * 1: [0,1,2,2] 
  * 2: [1,0,1,1] 
  * 3: [2,1,0,2] 
  * 4: [2,1,2,0]



Below is the tree from the second example interaction.

<image>

Lastly, here are the answers for querying every single node in example 2:

  * 1: [0,4,1,3,2] 
  * 2: [4,0,3,1,2] 
  * 3: [1,3,0,2,1] 
  * 4: [3,1,2,0,1] 
  * 5: [2,2,1,1,0]

Solution (in JAVA):

Solution:
import java.io.*;import java.util.*;import java.math.*;
public class Main
{
    public void tq()throws Exception
    {
        st=new StringTokenizer(bq.readLine());
        int tq=1;
        sb=new StringBuilder(1000000);
        o:
        while(tq-->0)
        {
            int n=i();
            pl("? 1");
            System.out.flush();
            int ar[]=ari(n);
            int e=0;
            int o=0;
            for(int x=0;x<n;x++)
            {
                if(ar[x]!=0)
                {
                    if(ar[x]%2==0)e++;
                    else o++;
                }
            }
            if(e<o)
            {
                for(int x=0;x<n;x++)
                {
                    if(ar[x]==1)sl("1 "+(x+1));
                }
                for(int x=0;x<n;x++)
                {
                    if(ar[x]!=0)
                    {
                        if(ar[x]%2==0)
                        {
                            pl("? "+(x+1));
                            System.out.flush();
                            int r[]=ari(n);
                            for(int xa=0;xa<n;xa++)
                            {
                                if(r[xa]==1)sl((x+1)+" "+(xa+1));
                            }
                        }
                    }
                }
            }
            else
            {
                for(int x=0;x<n;x++)
                {
                    if(ar[x]!=0)
                    {
                        if(ar[x]%2!=0)
                        {
                            pl("? "+(x+1));
                            System.out.flush();
                            int r[]=ari(n);
                            for(int xa=0;xa<n;xa++)
                            {
                                if(r[xa]==1)sl((x+1)+" "+(xa+1));
                            }
                        }
                    }
                }
            }
        }
        pl("!");
        p(sb);
        System.out.flush();
    }

    long mod=1000000007l;int max=Integer.MAX_VALUE,min=Integer.MIN_VALUE;
    long maxl=Long.MAX_VALUE,minl=Long.MIN_VALUE;
    BufferedReader bq=new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer st;StringBuilder sb;
    public static void main(String[] a)throws Exception{new Main().tq();}
    int[] so(int ar[]){Integer r[]=new Integer[ar.length];for(int x=0;x<ar.length;x++)r[x]=ar[x];
        Arrays.sort(r);for(int x=0;x<ar.length;x++)ar[x]=r[x];return ar;}
    long[] so(long ar[]){Long r[]=new Long[ar.length];for(int x=0;x<ar.length;x++)r[x]=ar[x];
        Arrays.sort(r);for(int x=0;x<ar.length;x++)ar[x]=r[x];return ar;}
    char[] so(char ar[])
    {Character r[]=new Character[ar.length];for(int x=0;x<ar.length;x++)r[x]=ar[x];
        Arrays.sort(r);for(int x=0;x<ar.length;x++)ar[x]=r[x];return ar;}
    void s(String s){sb.append(s);}void s(int s){sb.append(s);}void s(long s){sb.append(s);}
    void s(char s){sb.append(s);}void s(double s){sb.append(s);}
    void ss(){sb.append(' ');}void sl(String s){sb.append(s);sb.append("\n");}
    void sl(int s){sb.append(s);sb.append("\n");}
    void sl(long s){sb.append(s);sb.append("\n");}void sl(char s){sb.append(s);sb.append("\n");}
    void sl(double s){sb.append(s);sb.append("\n");}void sl(){sb.append("\n");}
    int l(int v){return 31-Integer.numberOfLeadingZeros(v);}
    long l(long v){return 63-Long.numberOfLeadingZeros(v);}
    int min(int a,int b){return a<b?a:b;}
    int min(int a,int b,int c){return a<b?a<c?a:c:b<c?b:c;}
    int max(int a,int b){return a>b?a:b;}
    int max(int a,int b,int c){return a>b?a>c?a:c:b>c?b:c;}
    long min(long a,long b){return a<b?a:b;}
    long min(long a,long b,long c){return a<b?a<c?a:c:b<c?b:c;}
    long max(long a,long b){return a>b?a:b;}
    long max(long a,long b,long c){return a>b?a>c?a:c:b>c?b:c;}
    int abs(int a){return Math.abs(a);}
    long abs(long a){return Math.abs(a);}
    int sq(int a){return (int)Math.sqrt(a);}long sq(long a){return (long)Math.sqrt(a);}
    long gcd(long a,long b){while(b>0l){long c=a%b;a=b;b=c;}return a;}
    int gcd(int a,int b){while(b>0){int c=a%b;a=b;b=c;}return a;}
    boolean pa(String s,int i,int j){while(i<j)if(s.charAt(i++)!=s.charAt(j--))return false;return true;}
    boolean[] si(int n)
    {boolean bo[]=new boolean[n+1];bo[0]=true;bo[1]=true;for(int x=4;x<=n;x+=2)bo[x]=true;
        for(int x=3;x*x<=n;x+=2){if(!bo[x]){int vv=(x<<1);for(int y=x*x;y<=n;y+=vv)bo[y]=true;}}
        return bo;}long mul(long a,long b,long m)
{long r=1l;a%=m;while(b>0){if((b&1)==1)r=(r*a)%m;b>>=1;a=(a*a)%m;}return r;}
    int i()throws IOException{if(!st.hasMoreTokens())st=new StringTokenizer(bq.readLine());
        return Integer.parseInt(st.nextToken());}
    long l()throws IOException{if(!st.hasMoreTokens())st=new StringTokenizer(bq.readLine());
        return Long.parseLong(st.nextToken());}String s()throws IOException
{if(!st.hasMoreTokens())st=new StringTokenizer(bq.readLine());return st.nextToken();}
    double d()throws IOException{if(!st.hasMoreTokens())st=new StringTokenizer(bq.readLine());
        return Double.parseDouble(st.nextToken());}void p(Object p){System.out.print(p);}
    void p(String p){System.out.print(p);}void p(int p){System.out.print(p);}
    void p(double p){System.out.print(p);}void p(long p){System.out.print(p);}
    void p(char p){System.out.print(p);}void p(boolean p){System.out.print(p);}
    void pl(Object p){System.out.println(p);}void pl(String p){System.out.println(p);}
    void pl(int p){System.out.println(p);}void pl(char p){System.out.println(p);}
    void pl(double p){System.out.println(p);}void pl(long p){System.out.println(p);}
    void pl(boolean p){System.out.println(p);}void pl(){System.out.println();}
    void s(int a[]){for(int e:a){sb.append(e);sb.append(' ');}sb.append("\n");}
    void s(long a[]){for(long e:a){sb.append(e);sb.append(' ');}sb.append("\n");}
    void s(int ar[][]){for(int a[]:ar){for(int e:a){sb.append(e);sb.append(' ');}sb.append("\n");}}
    void s(char a[]){for(char e:a){sb.append(e);sb.append(' ');}sb.append("\n");}
    void s(char ar[][]){for(char a[]:ar){for(char e:a){sb.append(e);}sb.append("\n");}}
    int[] ari(int n)throws IOException
    {int ar[]=new int[n];if(!st.hasMoreTokens())st=new StringTokenizer(bq.readLine());
        for(int x=0;x<n;x++)ar[x]=Integer.parseInt(st.nextToken());return ar;}
    int[][] ari(int n,int m)throws IOException
    {int ar[][]=new int[n][m];for(int x=0;x<n;x++){if(!st.hasMoreTokens())st=new StringTokenizer(bq.readLine());
        for(int y=0;y<m;y++)ar[x][y]=Integer.parseInt(st.nextToken());}return ar;}
    long[] arl(int n)throws IOException
    {long ar[]=new long[n];if(!st.hasMoreTokens())st=new StringTokenizer(bq.readLine());
        for(int x=0;x<n;x++) ar[x]=Long.parseLong(st.nextToken());return ar;}
    long[][] arl(int n,int m)throws IOException
    {long ar[][]=new long[n][m];for(int x=0;x<n;x++)
    {if(!st.hasMoreTokens())st=new StringTokenizer(bq.readLine());
        for(int y=0;y<m;y++)ar[x][y]=Long.parseLong(st.nextToken());}return ar;}
    String[] ars(int n)throws IOException
    {String ar[]=new String[n];if(!st.hasMoreTokens())st=new StringTokenizer(bq.readLine());
        for(int x=0;x<n;x++) ar[x]=st.nextToken();return ar;}
    double[] ard(int n)throws IOException
    {double ar[]=new double[n];if(!st.hasMoreTokens())st=new StringTokenizer(bq.readLine());
        for(int x=0;x<n;x++)ar[x]=Double.parseDouble(st.nextToken());return ar;}
    double[][] ard(int n,int m)throws IOException
    {double ar[][]=new double[n][m];for(int x=0;x<n;x++)
    {if(!st.hasMoreTokens())st=new StringTokenizer(bq.readLine());
        for(int y=0;y<m;y++)ar[x][y]=Double.parseDouble(st.nextToken());}return ar;}
    char[] arc(int n)throws IOException{char ar[]=new char[n];if(!st.hasMoreTokens())st=new StringTokenizer(bq.readLine());
        for(int x=0;x<n;x++)ar[x]=st.nextToken().charAt(0);return ar;}
    char[][] arc(int n,int m)throws IOException{char ar[][]=new char[n][m];
        for(int x=0;x<n;x++){String s=bq.readLine();for(int y=0;y<m;y++)ar[x][y]=s.charAt(y);}return ar;}
    void p(int ar[]){StringBuilder sb=new StringBuilder(2*ar.length);
        for(int a:ar){sb.append(a);sb.append(' ');}System.out.println(sb);}
    void p(int ar[][]){StringBuilder sb=new StringBuilder(2*ar.length*ar[0].length);
        for(int a[]:ar){for(int aa:a){sb.append(aa);sb.append(' ');}sb.append("\n");}p(sb);}
    void p(long ar[]){StringBuilder sb=new StringBuilder(2*ar.length);
        for(long a:ar){sb.append(a);sb.append(' ');}System.out.println(sb);}
    void p(long ar[][]){StringBuilder sb=new StringBuilder(2*ar.length*ar[0].length);
        for(long a[]:ar){for(long aa:a){sb.append(aa);sb.append(' ');}sb.append("\n");}p(sb);}
    void p(String ar[]){int c=0;for(String s:ar)c+=s.length()+1;StringBuilder sb=new StringBuilder(c);
        for(String a:ar){sb.append(a);sb.append(' ');}System.out.println(sb);}
    void p(double ar[]){StringBuilder sb=new StringBuilder(2*ar.length);
        for(double a:ar){sb.append(a);sb.append(' ');}System.out.println(sb);}
    void p(double ar[][]){StringBuilder sb=new StringBuilder(2*ar.length*ar[0].length);
        for(double a[]:ar){for(double aa:a){sb.append(aa);sb.append(' ');}sb.append("\n");}p(sb);}
    void p(char ar[]){StringBuilder sb=new StringBuilder(2*ar.length);
        for(char aa:ar){sb.append(aa);sb.append(' ');}System.out.println(sb);}
    void p(char ar[][]){StringBuilder sb=new StringBuilder(2*ar.length*ar[0].length);
        for(char a[]:ar){for(char aa:a){sb.append(aa);sb.append(' ');}sb.append("\n");}p(sb);}
}