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.util.*;
import java.util.Map.Entry;


import java.io.*;
import java.math.*;
import static java.util.stream.Collectors.*;
import static java.util.Map.Entry.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
	static long mod=(long) (1e9+7);  
	public static void main (String[] args) throws Exception
	{
		
		final long mod1=(long) 998244353;
		Reader s=new Reader();
		  PrintWriter pt=new PrintWriter(System.out);
		  
		  BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
//		  int T=s.nextInt();
//		  int T=Integer.parseInt(br.readLine());
		  int T=1;
		  
		  while(T-->0)
		  {
			  int n=s.nextInt();
			  int e=0;
			  Deque<Integer> q = new ArrayDeque<Integer>();
			  HashSet<Integer> adj[]=new HashSet[n+1];
			  for(int i=0;i<=n;i++) {
				  adj[i]=new HashSet<Integer>();
			  }
			  
			  
			  
			  int h=1;
			  System.out.println("? "+h);
			  System.out.flush();
			  StringTokenizer st=new StringTokenizer(br.readLine(), " ");
			  int k[]=new int[n];
			  for(int i=1;i<=n;i++) {
				  
				  k[i-1]=Integer.parseInt(st.nextToken());
				  if(k[i-1]==1) {
					  if(h<i) {
						  if(!adj[h].contains(i)) {
							  e++;
							  adj[h].add(i);
						  }
						  
					  }
					  else {
						  if(!adj[i].contains(h)) {
							  e++;
							  adj[i].add(h);
						  }
					  }
				  }
			  }	  
			  
			  int even=0, odd=0;
			  for(int j=0;j<n;j++) {
				  if(k[j]%2==0)
					  even++;
				  else
					  odd++;
			  }
			  if(even<=odd) {
				  for(int j=0;j<n;j++) {
					  if(k[j]%2==0&&k[j]!=0) {
						  q.add(j+1);
					  }
				  }
			  }
			  else {
				  for(int j=0;j<n;j++) {
					  if(k[j]%2==1&&k[j]!=0) {
						  q.add(j+1);
					  }
				  }
			  }
			  
			  
			  
			  
			  while(!q.isEmpty()&&e<n-1) {
				  h=q.poll();
				  System.out.println("? "+h);
				  System.out.flush();
				  st=new StringTokenizer(br.readLine(), " ");
				  k=new int[n];
				  for(int i=1;i<=n;i++) {
					  k[i-1]=Integer.parseInt(st.nextToken());
					  if(k[i-1]==1) {
						  if(h<i) {
							  if(!adj[h].contains(i)) {
								  e++;
								  adj[h].add(i);
							  }
							  
						  }
						  else {
							  if(!adj[i].contains(h)) {
								  e++;
								  adj[i].add(h);
							  }
						  }
					  }
				  }
			  }
			  System.out.println("!");
			  for(int i=1;i<=n;i++) {
				  for(int j:adj[i]) {
					  System.out.println(i+" "+j);
				  }
			  }
			  System.out.flush();

			  
		  }
		  pt.close();
	}
	
	public static int getFreq(int arr[], int n) {
		int k=0;
		for(int i=0;i<arr.length;i++) {
			if(arr[i]==n)
				k++;
		}
		return k;
	}
	
	public static void primeFactors(int n)
    {
        // Print the number of 2s that divide n
		HashMap<Integer, Integer> hm=new HashMap<Integer, Integer>();
        while (n%2==0)
        {
            hm.put(2, hm.getOrDefault(2, 0)+1);
            n/=2;
        }
 
        // n must be odd at this point.  So we can
        // skip one element (Note i = i +2)
        for (int i = 3; i <= Math.sqrt(n); i+= 2)
        {
            // While i divides n, print i and divide n
            while (n%i == 0)
            {
                n /= i;
                hm.put(i, hm.getOrDefault(i, 0)+1);
            }
        }
 
        // This condition is to handle the case whien
        // n is a prime number greater than 2
        if (n > 2)
        	hm.put(n, hm.getOrDefault(n, 0)+1);
    }


	
	static boolean isPartition(int arr[], int n) {
		int sum = 0;
	    int i, j;
	 
	    // Calculate sum of all elements
	    for (i = 0; i < n; i++)
	        sum += arr[i];
	 
	    if (sum % 2 != 0)
	        return false;
	 
	    boolean part[][]=new boolean[sum/2+1][n+1];
	 
	    // initialize top row as true
	    for (i = 0; i <= n; i++)
	        part[0][i] = true;
	 
	    // initialize leftmost column, except part[0][0], as false
	    for (i = 1; i <= sum / 2; i++)
	        part[i][0] = false;
	 
	    // Fill the partition table in bottom up manner
	    for (i = 1; i <= sum / 2; i++) {
	        for (j = 1; j <= n; j++) {
	            part[i][j] = part[i][j - 1];
	            if (i >= arr[j - 1])
	                part[i][j] = part[i][j]
	                             || part[i - arr[j - 1]][j - 1];
	        }
	    }
	    return part[sum / 2][n];
	}
	
	static int setBit(int S, int j) { return S | 1 << j; }

	static int clearBit(int S, int j) { return S & ~(1 << j); }

	static int toggleBit(int S, int j) { return S ^ 1 << j; }

	static boolean isOn(int S, int j) { return (S & 1 << j) != 0; }

	static int turnOnLastZero(int S) { return S | S + 1; }
	
	static int turnOnLastConsecutiveZeroes(int S) { return S | S - 1; }
	
	static int turnOffLastBit(int S) { return S & S - 1; }
	
	static int turnOffLastConsecutiveBits(int S) { return S & S + 1; }

	static int lowBit(int S) { return S & -S; }

	static int setAll(int N) { return (1 << N) - 1; }

	static int modulo(int S, int N) { return (S & N - 1); }		 //S%N, N is a power of 2

	static boolean isPowerOfTwo(int S) { return (S & S - 1) == 0; }
	
	static boolean isWithin(long x, long y, long d, long k) {
		return x*k*x*k + y*k*y*k <= d*d;
	}
	
	static long modFact(long n, 
            long p) 
	{ 
		if (n >= p) 
		 return 0; 
		
		long result = 1; 
		for (int i = 1; i <= n; i++) 
		 result = (result * i) % p; 
		
		return result; 
	} 
	static int sum(int[] arr, int n)
	{
	    int inc[]=new int[n+1];
	    int dec[]=new int[n+1];
	    inc[0] = arr[0];
	    dec[0] = arr[0];

	    for (int i = 1; i < n; i++) {
	        for (int j = 0; j < i; j++) {
	            if (arr[j] > arr[i]) {
	                dec[i] = max(dec[i], inc[j] + arr[i]);
	            }
	            else if (arr[i] > arr[j]) {
	                inc[i] = max(inc[i], dec[j] + arr[i]);
	            }
	        }
	    }
	    return max(inc[n - 1], dec[n - 1]);
	}
	static long nc2(long a) {
		return a*(a-1)/2;
	}
	public static int numberOfprimeFactors(int n) 
    { 
        // Print the number of 2s that divide n 
		HashSet<Integer> hs = new HashSet<Integer>();
        while (n%2==0) 
        { 
            hs.add(2);
            n /= 2; 
        } 
  
        // n must be odd at this point.  So we can 
        // skip one element (Note i = i +2) 
        for (int i = 3; i <= Math.sqrt(n); i+= 2) 
        { 
            // While i divides n, print i and divide n 
            while (n%i == 0) 
            { 
                hs.add(i);
                n /= i; 
            } 
        } 
  
        // This condition is to handle the case whien 
        // n is a prime number greater than 2 
        if (n > 2) 
            hs.add(n);
        return hs.size();
    } 
	static long gcd(long a, long b) 
    { 
      if (b == 0) 
        return a; 
      return gcd(b, a % b);  
    } 




	

	static void reverse(int arr[],int start, int end) 
	{ 
		int temp; 
		   
		while (start < end) 
		{ 
		    temp = arr[start];  
		    arr[start] = arr[end]; 
		    arr[end] = temp; 
		    start++; 
		    end--; 
		}  
	}  
	static void reverse(long arr[],int start, int end) 
	{ 
		long temp; 
		   
		while (start < end) 
		{ 
		    temp = arr[start];  
		    arr[start] = arr[end]; 
		    arr[end] = temp; 
		    start++; 
		    end--; 
		}  
	}  
	static boolean isPrime(int n) 
    { 
        // Corner cases 
        if (n <= 1) return false; 
        if (n <= 3) return true; 
      
        // This is checked so that we can skip  
        // middle five numbers in below loop 
        if (n % 2 == 0 || n % 3 == 0) return false; 
      
        for (int i = 5; i * i <= n; i = i + 6) 
            if (n % i == 0 || n % (i + 2) == 0) 
            return false; 
      
        return true; 
    } 
	static int p2(int n) {
		int k=0;
		while(n>1) {
			if(n%2!=0)
				return k;
			n/=2;
			k++;
		}
		return k;
	}
	static boolean isp2(int n) {
		while(n>1) {
			if(n%2==1)
				return false;
			n/=2;
		}
		return true;
	}
	static int binarySearch(int arr[], int first, int last, int key){  
		   int mid = (first + last)/2;  
		   while( first <= last ){  
		      if ( arr[mid] < key ){  
		        first = mid + 1;     
		      }else if ( arr[mid] == key ){  
		        return mid;  
		      }else{  
		         last = mid - 1;  
		      }  
		      mid = (first + last)/2;  
		   }  
		   return -1;
		 }  

	static void print(int a[][]) {
		for(int i=0;i<a.length;i++)
		{
			for(int j=0;j<a[0].length;j++)
				System.out.print(a[i][j]+" ");
			System.out.println();
		}
	}
	static int max (int x, int y) {
		return (x > y)? x : y;
	} 
	static int search(Pair[] p, Pair pair) {
		int l=0, r=p.length;
		while (l <= r) { 
	        int m = l + (r - l) / 2;
	        if (p[m].compareTo(pair)==0) 
	            return m; 
	        if (p[m].compareTo(pair)<0) 
	            l = m + 1; 
	        else
	            r = m - 1;
	    }
	    return -1;
	}
	static void pa(int a[])
	{
		for(int i=0;i<a.length;i++)
			System.out.print(a[i]+" ");
		System.out.println();
		
	}
	static void pa(long a[])
	{
		for(int i=0;i<a.length;i++)
			System.out.print(a[i]+" ");
		System.out.println();
		
	}
	static void reverseArray(int arr[], 
            int start, int end) 
	{ 
		int temp; 
		   
		while (start < end) 
		{ 
		    temp = arr[start];  
		    arr[start] = arr[end]; 
		    arr[end] = temp; 
		    start++; 
		    end--; 
		}  
	}     
	static boolean isPalindrome(String s) {
		int l=s.length();
		for(int i=0;i<l/2;i++)
		{
			if(s.charAt(i)!=s.charAt(l-i-1))
				return false;
		}
		return true;
	}
	static long nc2(long n, long m) {
		return (n*(n-1)/2)%m;
	}
	static long c(long a) {
		return a*(a+1)/2;
	}
	static int next(int[] arr, int target)  
    {  
        int start = 0, end = arr.length - 1;  
    
        int ans = -1;  
        while (start <= end) {  
            int mid = (start + end) / 2;  
    
            // Move to right side if target is  
            // greater.  
            if (arr[mid] < target) {
                start = mid + 1;  
            }  
    
            // Move left side.  
            else {  
                ans = mid;  
                end = mid - 1;  
            }  
        }  
        return ans;  
    } 
	
	static int prev(int[] arr, int target)  
    {  
        int start = 0, end = arr.length - 1;  
    
        int ans = -1;  
        while (start <= end) {  
            int mid = (start + end) / 2;  
    
            // Move to left side if target is  
            // lesser.  
            if (arr[mid] > target) {
                end = mid - 1;  
            }  
    
            // Move right side.  
            else {  
                ans = mid;  
                start = mid + 1;  
            }  
        }  
        return ans;  
    } 

	static long power(long x, long y, long p) 
    { 
        long res = 1; 
        x = x % p; 
                      
        while (y > 0) 
        { 
            if (y % 2 == 1) 
                res = (res * x) % p; 
            y = y >> 1;
            x = (x * x) % p; 
        } 
        return  res; 
    } 
    static long modInverse(long n, long p) 
    { 
        return power(n, p-2, p); 
    } 
    static long nCrModP(long n, long r, 
                                    long p) 
    { 
        if(r>n)
        	return 0;
    	if (r == 0) 
            return 1; 
        long[] fac = new long[(int) (n+1)]; 
        fac[0] = 1; 
        for (int i = 1 ;i <= n; i++) 
            fac[i] = fac[i-1] * i % p;
        return (fac[(int) n]* modInverse(fac[(int) r], p) 
                % p * modInverse(fac[(int) (n-r)], p) 
                                    % p) % p; 
    } 
	static String reverse(String str)
	{
		return new StringBuffer(str).reverse().toString();
	}



	static long fastpow(long x, long y, long m)  
    { 
        if (y == 0) 
            return 1; 
          
        long p = fastpow(x, y / 2, m) % m; 
        p = (p * p) % m; 
      
        if (y % 2 == 0) 
            return p; 
        else
            return (x * p) % m; 
    } 
	
	static boolean isPerfectSquare(long l)
	{
		return Math.pow((long)Math.sqrt(l),2)==l;
	}
	
	
	static void merge(long[] arr, int l, int m, int r) 
    { 
        // Find sizes of two subarrays to be merged 
        int n1 = m - l + 1; 
        int n2 = r - m; 
  
        /* Create temp arrays */
        long L[] = new long [n1]; 
        long R[] = new long [n2]; 
  
        /*Copy data to temp arrays*/
        for (int i=0; i<n1; ++i) 
            L[i] = arr[l + i]; 
        for (int j=0; j<n2; ++j) 
            R[j] = arr[m + 1+ j]; 
  
  
        /* Merge the temp arrays */
  
        // Initial indexes of first and second subarrays 
        int i = 0, j = 0; 
  
        // Initial index of merged subarry array 
        int k = l; 
        while (i < n1 && j < n2) 
        { 
            if (L[i] <= R[j]) 
            { 
                arr[k] = L[i]; 
                i++; 
            } 
            else
            { 
                arr[k] = R[j]; 
                j++; 
            } 
            k++; 
        } 
  
        /* Copy remaining elements of L[] if any */
        while (i < n1) 
        { 
            arr[k] = L[i]; 
            i++; 
            k++; 
        } 
  
        /* Copy remaining elements of R[] if any */
        while (j < n2) 
        { 
            arr[k] = R[j]; 
            j++; 
            k++; 
        } 
    } 
  
    // Main function that sorts arr[l..r] using 
    // merge() 
    static void sort(int arr[], int l, int r) 
    { 
        if (l < r) 
        { 
            // Find the middle point 
            int m = (l+r)/2; 
  
            // Sort first and second halves 
            sort(arr, l, m); 
            sort(arr , m+1, r); 
  
            // Merge the sorted halves 
            merge(arr, l, m, r); 
        } 
    } 
	static void merge(int arr[], int l, int m, int r) 
    { 
        // Find sizes of two subarrays to be merged 
        int n1 = m - l + 1; 
        int n2 = r - m; 
  
        /* Create temp arrays */
        int L[] = new int [n1]; 
        int R[] = new int [n2]; 
  
        /*Copy data to temp arrays*/
        for (int i=0; i<n1; ++i) 
            L[i] = arr[l + i]; 
        for (int j=0; j<n2; ++j) 
            R[j] = arr[m + 1+ j]; 
  
  
        /* Merge the temp arrays */
  
        // Initial indexes of first and second subarrays 
        int i = 0, j = 0; 
  
        // Initial index of merged subarry array 
        int k = l; 
        while (i < n1 && j < n2) 
        { 
            if (L[i] <= R[j]) 
            { 
                arr[k] = L[i]; 
                i++; 
            } 
            else
            { 
                arr[k] = R[j]; 
                j++; 
            } 
            k++; 
        } 
  
        /* Copy remaining elements of L[] if any */
        while (i < n1) 
        { 
            arr[k] = L[i]; 
            i++; 
            k++; 
        } 
  
        /* Copy remaining elements of R[] if any */
        while (j < n2) 
        { 
            arr[k] = R[j]; 
            j++; 
            k++; 
        } 
    } 
  
    // Main function that sorts arr[l..r] using 
    // merge() 
    static void sort(long arr[], int l, int r) 
    { 
        if (l < r) 
        { 
            // Find the middle point 
            int m = (l+r)/2; 
  
            // Sort first and second halves 
            sort(arr, l, m); 
            sort(arr , m+1, r); 
  
            // Merge the sorted halves 
            merge(arr, l, m, r); 
        } 
    } 
    static class Pair implements Comparable<Pair>{
        int a;
        int b;
        Pair(int a,int b){
            this.a=a;
 
            this.b=b;
        }   
        public int compareTo(Pair p){
            if(a>p.a)
                return 1;
            if(a==p.a)
                return (b-p.b);
            return -1;
        }
    }
	static class Reader 
    { 
        final private int BUFFER_SIZE = 1 << 16; 
        private DataInputStream din; 
        private byte[] buffer; 
        private int bufferPointer, bytesRead; 
  
        public Reader() 
        { 
            din = new DataInputStream(System.in); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public Reader(String file_name) throws IOException 
        { 
            din = new DataInputStream(new FileInputStream(file_name)); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public String readLine() throws IOException 
        { 
            byte[] buf = new byte[128]; // line length 
            int cnt = 0, c; 
            while ((c = read()) != -1) 
            { 
                if (c == '\n') 
                    break; 
                buf[cnt++] = (byte) c; 
            } 
            return new String(buf, 0, cnt); 
        } 
  
        public int nextInt() throws IOException 
        { 
            int ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do
            { 
                ret = ret * 10 + c - '0'; 
            }  while ((c = read()) >= '0' && c <= '9'); 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public long nextLong() throws IOException 
        { 
            long ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public double nextDouble() throws IOException 
        { 
            double ret = 0, div = 1; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
  
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
  
            if (c == '.') 
            { 
                while ((c = read()) >= '0' && c <= '9') 
                { 
                    ret += (c - '0') / (div *= 10); 
                } 
            } 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        private void fillBuffer() throws IOException 
        { 
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
            if (bytesRead == -1) 
                buffer[0] = -1; 
        } 
  
        private byte read() throws IOException 
        { 
            if (bufferPointer == bytesRead) 
                fillBuffer(); 
            return buffer[bufferPointer++]; 
        } 
  
        public void close() throws IOException 
        { 
            if (din == null) 
                return; 
            din.close(); 
        } 
    } 
}