Problem: The Dogeforces company has k employees. Each employee, except for lower-level employees, has at least 2 subordinates. Lower-level employees have no subordinates. Each employee, except for the head of the company, has exactly one direct supervisor. The head of the company is a direct or indirect supervisor of all employees. It is known that in Dogeforces, each supervisor receives a salary strictly more than all his subordinates.

The full structure of the company is a secret, but you know the number of lower-level employees and for each pair of lower-level employees, the salary of their common supervisor is known (if there are several such supervisors, then the supervisor with the minimum salary). You have to restore the structure of the company.

Input

The first line contains a single integer n (2 ≤ n ≤ 500) — the number of lower-level employees.

This is followed by n lines, where i-th line contains n integers a_{i,1}, a_{i,2}, ..., a_{i,n} (1 ≤ a_{i,j} ≤ 5000) — salary of the common supervisor of employees with numbers i and j. It is guaranteed that a_{i,j} = a_{j,i}. Note that a_{i,i} is equal to the salary of the i-th employee.

Output

In the first line, print a single integer k — the number of employees in the company.

In the second line, print k integers c_1, c_2, ..., c_k, where c_i is the salary of the employee with the number i.

In the third line, print a single integer r — the number of the employee who is the head of the company.

In the following k-1 lines, print two integers v and u (1 ≤ v, u ≤ k) — the number of the employee and his direct supervisor.

Note that the lower-level employees have numbers from 1 to n, and for the rest of the employees, you have to assign numbers from n+1 to k. If there are several correct company structures, you can print any of them.

Example

Input


3
2 5 7
5 1 7
7 7 4


Output


5
2 1 4 7 5 
4
1 5
2 5
5 4
3 4

Note

One of the possible structures in the first example: <image>

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.PriorityQueue;
import java.util.Random;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

@SuppressWarnings("unused")
public class Solution{
	
	static final int N = 505;
	static int[][] a;
	static ArrayList<int[]> e;
	static int[] c;
	static int n;
	
	
	public static void main(String[] args) throws IOException {
    	
		
    	FastScanner fs = new FastScanner();
    	PrintWriter out = new PrintWriter(System.out);
    	
    		
    	int tt = 1;
    	outer:
    	while(tt-->0) {
    		
    		n = fs.nextInt();
    		a = new int[n][n];
    		c = new int[2*n];
    		
    		e = new ArrayList<int[]>();
    		
    		for(int i=0;i<n;i++) {
    			for(int j=0;j<n;j++) {
    				a[i][j] = fs.nextInt();
    			}
    		}
    		
    		
    		for(int i=0;i<n;i++) c[i] = a[i][i];
    		
    		ArrayList<Integer> list = new ArrayList<>();
    		for(int i=0;i<n;i++) list.add(i);
    		
    		int root = calc(list);
    		
    		out.println(n);
    		for(int i=0;i<n;i++) out.print(c[i]+" ");
    		out.println();
    		out.println(root+1);
    		
    		for(int[] ar: e) {
    			out.println((ar[0]+1)+" "+(ar[1]+1));
    		}
    		
    		
    		
    		
    	}
    	
    	out.close();
    	
    }
	
	
	
	static int calc(ArrayList<Integer> list) {
		if(list.size()==1) {
			return list.get(0);
		}
		
		int res = -1;
		int init = list.get(0);
		
		for(int u: list) {
			res = Math.max(res, a[init][u]);
		}
		
		ArrayList<ArrayList<Integer>> g = new ArrayList<>();
		ArrayList<Integer> frst = new ArrayList<>(); frst.add(init);
		g.add(frst);
		
		for(int i=1;i<list.size();i++) {
			int v = list.get(i);
			int grp = -1;
			for(int j=0;j<g.size();j++) {
				if(a[v][g.get(j).get(0)]!=res) {
					grp = j; break;
				}
			}
			if(grp==-1) {
				grp = g.size();
				ArrayList<Integer> k = new ArrayList<>();
				g.add(k);
			}
			g.get(grp).add(v);
		}
		
		int v = n++;
		c[v] = res;
		
		for(ArrayList<Integer> l: g) {
			int u = calc(l);
			e.add(new int[] {u, v});
		}
		return v;
	}
	
	
	
    
    
    static final Random random=new Random();
    
    static <T> void shuffle(T[] arr) {
    	int n = arr.length;
    	for(int i=0;i<n;i++	) {
    		int k = random.nextInt(n);
    		T temp = arr[k]; arr[k] = arr[i]; arr[i] = temp;
    	}
    }
    
    	
    static void ruffleSort(int[] a) {
    	int n=a.length;//shuffle, then sort 
    	for (int i=0; i<n; i++) {
    		int oi=random.nextInt(n); int temp=a[oi];
    		a[oi]=a[i]; a[i]=temp;
    	}
    	Arrays.sort(a);
    }
    
    static void ruffleSort(long[] a) {
    	int n=a.length;//shuffle, then sort 
    	for (int i=0; i<n; i++) {
    		int oi=random.nextInt(n); long temp=a[oi];
    		a[oi]=a[i]; a[i]=temp;
    	}
    	Arrays.sort(a);
    }
   
  
    
    static void reverse(int[] arr, int l, int r) {
    	for(int i=l;i<l+(r-l)/2;i++){
    		int temp = arr[i]; arr[i] = arr[r-i+l-1]; arr[r-i+l-1] = temp;
    	}
    }
    
    static void reverse(long[] arr, int l, int r) {
    	for(int i=l;i<l+(r-l)/2;i++){
    		long temp = arr[i]; arr[i] = arr[r-i+l-1]; arr[r-i+l-1] = temp;
    	}
    }
    
    
    static <T> void reverse(T[] arr, int l, int r) {
    	for(int i=l;i<l+(r-l)/2;i++) {
    		T temp = arr[i]; arr[i] = arr[r-i+l-1]; arr[r-i+l-1] = temp;
    	}
    }
    	
    	
    static class FastScanner{
    	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    	StringTokenizer st = new StringTokenizer("");
     
    	public String next(){
    		while(!st.hasMoreElements()){
    			try{
    				st = new StringTokenizer(br.readLine());
    			} catch(IOException e){
    				e.printStackTrace();
    			}
    		}
    		return st.nextToken();
    	}
    		
    	public String nextLine() throws IOException {
    		return br.readLine();
    	}
    		
    	public int nextInt(){
    		return Integer.parseInt(next());
    	}
     
    	public int[] readArray(int n){
    		int[] a = new int[n];
    		for(int i=0;i<n;i++)
    			a[i] = nextInt();
    		return a;
    	}
    		
    	public long nextLong() {
    		return Long.parseLong(next());
    	}
    		
    	public char nextChar() {
    		return next().toCharArray()[0];
    	}
    }
   	
}