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.util.*;

import java.io.*;

public class Main {
	public static void main(String[] args) throws Exception {

		int n=sc.nextInt();
		UnionFind u=new UnionFind(n+20);
		int[][]a=new int[n][n];
		for(int i=0;i<n;i++)a[i]=sc.nextIntArray(n);
		PriorityQueue<tuble>pq=new PriorityQueue<Main.tuble>();
		int[]ans=new int[300000];
		int[]ans2=new int[300000];
		int free=0;
		
		for(int i=0;i<n;i++) {
			ans2[free]=a[i][i];
			
			free++;
		}
		for(int i=0;i<n;i++) {
			for(int j=0;j<n;j++) {
				if(i!=j) {
					pq.add(new tuble(a[i][j], i, j));
				}
			}
		}
		int num=n;
		HashMap<Integer, Integer>hm=new HashMap<Integer, Integer>();
		for(int i=0;i<n;i++) {
			hm.put(u.findSet(i), i);
		}
		while(!pq.isEmpty()) {
			tuble z=pq.poll();
			if(u.isSameSet(z.y, z.z))continue;
			if(ans2[hm.get(u.findSet(z.z))]==z.x) {
				ans[hm.get(u.findSet(z.y))]=hm.get(u.findSet(z.z));
				hm.put(u.findSet(z.y), hm.get(u.findSet(z.z)));
			}else if(ans2[hm.get(u.findSet(z.y))]==z.x) {
				ans[hm.get(u.findSet(z.z))]=hm.get(u.findSet(z.y));
				hm.put(u.findSet(z.z), hm.get(u.findSet(z.y)));
			}else {
			num++;
			ans2[free]=z.x;
			ans[hm.get(u.findSet(z.z))]=free;
			ans[hm.get(u.findSet(z.y))]=free;
			hm.put(u.findSet(z.z), free);
			hm.put(u.findSet(z.y), free);
			free++;
		
			}
			u.unionSet(z.y, z.z);
		}
		pw.println(num);
		for(int i=0;i<num;i++)pw.print(ans2[i]+" ");
		pw.println();
		pw.println(num);
		for(int i=0;i<num-1;i++) {
			pw.println(i+1+" "+(ans[i]+1));
		}
		pw.close();
	}

	public static class UnionFind {
		int[] p, rank, setSize;
		int numSets;

		public UnionFind(int N) {
			p = new int[numSets = N];
			rank = new int[N];
			setSize = new int[N];
			for (int i = 0; i < N; i++) {
				p[i] = i;
				setSize[i] = 1;
			}
		}

		public int findSet(int i) {
			return p[i] == i ? i : (p[i] = findSet(p[i]));
		}

		public boolean isSameSet(int i, int j) {
			return findSet(i) == findSet(j);
		}

		public void unionSet(int i, int j) {
			if (isSameSet(i, j))
				return;
			numSets--;
			int x = findSet(i), y = findSet(j);
			if (rank[x] > rank[y]) {
				p[y] = x;
				setSize[x] += setSize[y];
			} else {
				p[x] = y;
				setSize[y] += setSize[x];
				if (rank[x] == rank[y])
					rank[y]++;
			}
		}

		public int numDisjointSets() {
			return numSets;
		}

		public int sizeOfSet(int i) {
			return setSize[findSet(i)];
		}
	}
	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 {
			String x = next();
			StringBuilder sb = new StringBuilder("0");
			double res = 0, f = 1;
			boolean dec = false, neg = false;
			int start = 0;
			if (x.charAt(0) == '-') {
				neg = true;
				start++;
			}
			for (int i = start; i < x.length(); i++)
				if (x.charAt(i) == '.') {
					res = Long.parseLong(sb.toString());
					sb = new StringBuilder("0");
					dec = true;
				} else {
					sb.append(x.charAt(i));
					if (dec)
						f *= 10;
				}
			res += Long.parseLong(sb.toString()) / f;
			return res * (neg ? -1 : 1);
		}

		public long[] nextlongArray(int n) throws IOException {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}

		public Long[] nextLongArray(int n) throws IOException {
			Long[] a = new Long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}

		public int[] nextIntArray(int n) throws IOException {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		public Integer[] nextIntegerArray(int n) throws IOException {
			Integer[] a = new Integer[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

	}

	static class pair implements Comparable<pair> {
		long x;
		long y;

		public pair(long x, long y) {
			this.x = x;
			this.y = y;
		}

		public String toString() {
			return x + " " + y;
		}

		public boolean equals(Object o) {
			if (o instanceof pair) {
				pair p = (pair) o;
				return p.x == x && p.y == y;
			}
			return false;
		}

		public int hashCode() {
			return new Double(x).hashCode() * 31 + new Double(y).hashCode();
		}

		public int compareTo(pair other) {
			if (this.x == other.x) {
				return Long.compare(this.y, other.y);
			}
			return Long.compare(this.x, other.x);
		}
	}

	static class tuble implements Comparable<tuble> {
		int x;
		int y;
		int z;

		public tuble(int x, int y, int z) {
			this.x = x;
			this.y = y;
			this.z = z;
		}

		public String toString() {
			return x + " " + y + " " + z;
		}

		public int compareTo(tuble other) {
			if (this.x == other.x) {
				if (this.y == other.y) {
					return this.z - other.z;
				}
				return this.y - other.y;
			} else {
				return this.x - other.x;
			}
		}
	}

	static long mod = 1000000007;
	static Random rn = new Random();
	static Scanner sc = new Scanner(System.in);
	static PrintWriter pw = new PrintWriter(System.out);
}