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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Set;
import java.util.HashMap;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.List;
import java.util.StringTokenizer;
import java.util.Map;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastReader in = new FastReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DDogeforces solver = new DDogeforces();
        solver.solve(1, in, out);
        out.close();
    }

    static class DDogeforces {
        int[] fa;

        int fa(int root) {
            return fa[root] == root ? root : (fa[root] = fa(fa[root]));
        }

        public void solve(int testNumber, FastReader in, PrintWriter out) {

            int n = in.nextInt();
            int[][] a = new int[n + 1][n + 1];
            for (int i = 1; i <= n; i++) {
                for (int j = 1; j <= n; j++) {
                    a[i][j] = in.nextInt();
                }
            }

            List<Node> infos = new ArrayList<>();
            for (int i = 1; i <= n; i++) {
                for (int j = i + 1; j <= n; j++) {
                    infos.add(new Node(a[i][j], i, j));
                }
            }

            List<Node> nodes = new ArrayList<>();
            List<Node> edges = new ArrayList<>();
            int[] parent = new int[n + 1];
            for (int i = 1; i <= n; i++) {
                nodes.add(new Node(a[i][i], i, 0));
                parent[i] = i;
            }

            infos.sort((aa, bb) -> aa.val - bb.val);


            int r = 0;
            for (int l = 0; l < infos.size(); l = r) {
                r = l;
                while (r < infos.size() && infos.get(r).val == infos.get(l).val) r++;

                List<List<Integer>> llist = heap(infos, l, r, a);
                for (List<Integer> list : llist) {
                    Set<Integer> set = new HashSet<>();
                    int newP = nodes.size() + 1;
                    for (Integer info : list) {
                        set.add(parent[info]);
                    }
                    for (Integer info : list) {
                        parent[info] = newP;
                    }

                    for (Integer p : set) {
                        edges.add(new Node(-1, p, newP));
                    }
                    nodes.add(new Node(infos.get(l).val, newP, 0));
                }
//            Set<Integer> set = new HashSet<>();
//            int newP = nodes.size() + 1;
//            for (int i = l; i < r; i++) {
//                set.add(parent[infos.get(i).x]);
//                set.add(parent[infos.get(i).y]);
//            }
//            for (int i = l; i < r; i++) {
//                parent[infos.get(i).x] = newP;
//                parent[infos.get(i).y] = newP;
//            }
//
//            for (Integer p : set) {
//                edges.add(new Node(-1, p, newP));
//            }
//            nodes.add(new Node(infos.get(l).val, newP, 0));

            }

            if (nodes.size() != edges.size() + 1) {
                out.println("nodes.size=" + nodes.size() + " edges.size = " + edges.size());
                for (int i = 1; i <= n; i++) {
                    for (int j = 1; j <= n; j++) {
                        out.print(a[i][j] + " ");
                    }
                    out.println();
                }

            }

            out.println(nodes.size());
            for (Node node : nodes) {
                out.print(node.val + " ");
            }
            out.println();
            out.println(nodes.get(nodes.size() - 1).x);
            for (Node edge : edges) {
                out.println(edge.x + " " + edge.y);
            }
        }

        private List<List<Integer>> heap(List<Node> infos, int l, int r, int[][] a) {
            fa = new int[a.length];
            Arrays.setAll(fa, i -> i);
            for (int i = l; i < r; i++) {
                int x = infos.get(i).x;
                int y = infos.get(i).y;
                int fax = fa(x);
                int fay = fa(y);
                fa[fax] = fay;
            }

            Map<Integer, List<Integer>> map = new HashMap<>();
            for (int i = l; i < r; i++) {
                int x = infos.get(i).x;
                int y = infos.get(i).y;
                int fax = fa(x);
                List<Integer> list = map.getOrDefault(fax, new ArrayList<>());
                if (!list.contains(x)) list.add(x);
                if (!list.contains(y)) list.add(y);
                map.put(fax, list);
            }
            List<List<Integer>> llist = new ArrayList<>();
            map.forEach((k, v) -> {
                llist.add(v);
            });
            return llist;

        }

        class Node {
            int val;
            int x;
            int y;

            public Node(int val, int x, int y) {
                this.val = val;
                this.x = x;
                this.y = y;
            }

        }

    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st = new StringTokenizer("");

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public FastReader(InputStream in) {
            br = new BufferedReader(new InputStreamReader(in));
        }

        public String next() {
            while (st == null || (!st.hasMoreElements())) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }

            }
            return st.nextToken();
        }

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

    }
}