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.*;
import java.math.*;
import java.security.*;
import java.text.*;
import java.util.*;
import java.util.concurrent.*;
import java.util.function.*;
import java.util.regex.*;
import java.util.stream.*;
import static java.util.stream.Collectors.joining;
import static java.util.stream.Collectors.toList;




public class Main{

    //static long MOD = 1_000_000_007L;
    static long MOD = 998_244_353L;
    //static long MOD = 1_000_000_033L;
    static long inv2 = (MOD + 1) / 2;
    static long [] fac;
    static long [] pow;
    static long [] inv;
    static int[][] dir = new int[][]{{1, 0}, {0, 1}, {-1, 0}, {0, -1}};
    static long lMax = 0x3f3f3f3f3f3f3f3fL;
    static int iMax = 0x3f3f3f3f;
    static HashMap <Long, Long> memo = new HashMap();
    static MyScanner sc = new MyScanner();
    //static ArrayList <Integer> primes;

    static long[] pow2;
    //-----------PrintWriter for faster output---------------------------------
    public static PrintWriter out;
    public static void main(String[] args) {
        out = new PrintWriter(new BufferedOutputStream(System.out));
        // Start writing your solution here. -------------------------------------

        int nn = 300000;

        /*fac = new long[nn + 1];
        fac[1] = 1;
        for(int i = 2; i <= nn; i++)
            fac[i] = fac[i - 1] * 1L * i % MOD;*/

        /*pow = new long[nn + 1];
        pow[0] = 1L;
        for(int i = 1; i <= nn; i++)
            pow[i] = pow[i - 1] * 2L % MOD;
        pow[1] = 3L;*/

        /*pow2 = new long[nn + 1];
        pow2[0] = 1L;
        for(int i = 1; i <= nn; i++)
            pow2[i] = pow2[i - 1] * 2L % (MOD - 1);*/

        /*inv = new long[nn + 1];
        inv[1] = 1;
        for (int i = 2; i <= nn; ++i)
            inv[i] = (MOD - MOD / i) * inv[(int)(MOD % i)] % MOD;*/

        //primes = sieveOfEratosthenes(100001);

        int t = 1;
        //t = sc.ni();
        while(t-- > 0) {
            int res = solve();
            //out.println(res);
        }
        out.close();
    }
    static int[] parent = new int[1010];
    static int salary[] = new int[1010];

    static int solve() {
        /*String s = sc.nextLine();
        char[] c = s.toCharArray();
        int n = c.length;*/
        //int n = sc.ni();
        //long[] a =  new long[n];
        //for(int i = 0; i < n; i++) a[i] = sc.nl();
        int n = sc.ni();
        for(int i = 0; i < 1010; i++) parent[i] = i;
        int[][] a = new int[n + 1][n + 1];
        ArrayList <int[]> par[] = new ArrayList[5001];
        for(int i = 1; i <= 5000; i++) par[i] = new ArrayList<>();
        ArrayList <Integer> sal = new ArrayList();
        ArrayList <int[]> edges = new ArrayList<>();
        int total = n;
        for(int i = 1; i <= n; i++)
            for(int j = 1; j <= n; j++) {
                a[i][j] = sc.ni();
                if(i == j) salary[i] = a[i][i];
                else par[a[i][j]].add(new int[]{i, j});
            }
        for(int i = 1; i <= 5000; i++) {
            for(int[] pair : par[i]) {
                int i1 = pair[0], i2 = pair[1];
                int r1 = find(i1), r2 = find(i2);
                //out.println(i1 + " " + i2 + "    " + r1 + " " + r2);
                if(r1 != r2) {
                    if(salary[r1] == i) {
                        union(r2, r1);
                        edges.add(new int[]{r2, r1});
                    } else if(salary[r2] == i) {
                        union(r1, r2);
                        edges.add(new int[]{r1, r2});
                    } else {
                        total++;
                        salary[total] = i;
                        union(r1, total);
                        union(r2, total);
                        edges.add(new int[]{r1, total});
                        edges.add(new int[]{r2, total});
                    }
                }
            }
        }
        out.println(total);
        for(int i = 1; i <= total; i++) out.print(salary[i] + " ");
        out.println();
        out.println(total);
        for(int[] edge : edges) out.println(edge[0] + " " + edge[1]);
        return 0;
    }

    static int find(int i) {
        if(parent[i] != i) return parent[i] = find(parent[i]);
        return parent[i];
    }
    static void union(int i, int j) {
        int ri = find(i), rj = find(j);
        if(ri != rj) parent[ri] = rj;
    }



    // SegmentTree range min/max query From uwi
    public static class SegmentTreeRMQ {
        public int M, H, N;
        public int[] st;

        public SegmentTreeRMQ(int n)
        {
            N = n;
            M = Integer.highestOneBit(Math.max(N-1, 1))<<2;
            H = M>>>1;
            st = new int[M];
            Arrays.fill(st, 0, M, Integer.MAX_VALUE);
        }

        public SegmentTreeRMQ(int[] a)
        {
            N = a.length;
            M = Integer.highestOneBit(Math.max(N-1, 1))<<2;
            H = M>>>1;
            st = new int[M];
            for(int i = 0;i < N;i++){
                st[H+i] = a[i];
            }
            Arrays.fill(st, H+N, M, Integer.MAX_VALUE);
            for(int i = H-1;i >= 1;i--)propagate(i);
        }

        public void update(int pos, int x)
        {
            st[H+pos] = x;
            for(int i = (H+pos)>>>1;i >= 1;i >>>= 1)propagate(i);
        }

        private void propagate(int i)
        {
            st[i] = Math.min(st[2*i], st[2*i+1]);
        }

        public int minx(int l, int r){
            int min = Integer.MAX_VALUE;
            if(l >= r)return min;
            while(l != 0){
                int f = l&-l;
                if(l+f > r)break;
                int v = st[(H+l)/f];
                if(v < min)min = v;
                l += f;
            }

            while(l < r){
                int f = r&-r;
                int v = st[(H+r)/f-1];
                if(v < min)min = v;
                r -= f;
            }
            return min;
        }

        public int min(int l, int r){ return l >= r ? 0 : min(l, r, 0, H, 1);}

        private int min(int l, int r, int cl, int cr, int cur)
        {
            if(l <= cl && cr <= r){
                return st[cur];
            }else{
                int mid = cl+cr>>>1;
                int ret = Integer.MAX_VALUE;
                if(cl < r && l < mid){
                    ret = Math.min(ret, min(l, r, cl, mid, 2*cur));
                }
                if(mid < r && l < cr){
                    ret = Math.min(ret, min(l, r, mid, cr, 2*cur+1));
                }
                return ret;
            }
        }
    }

    public static char[] rev(char[] a){char[] b = new char[a.length];for(int i = 0;i < a.length;i++)b[a.length-1-i] = a[i];return b;}

    public static double dist(double a, double b){
        return Math.sqrt(a * a + b * b);
    }

    public static long inv(long a){
        return quickPOW(a, MOD - 2);
    }

    public class Interval {
        int start;
        int end;
        public Interval(int start, int end) {
            this.start = start;
            this.end = end;
        }
    }

    public static ArrayList<Integer> sieveOfEratosthenes(int n) {
        boolean prime[] = new boolean[n + 1];
        Arrays.fill(prime, true);
        for (int p = 2; p * p <= n; p++) {
            if (prime[p]) {
                for (int i = p * 2; i <= n; i += p) {
                    prime[i] = false;
                }
            }
        }
        ArrayList<Integer> primeNumbers = new ArrayList<>();
        for (int i = 2; i <= n; i++) {
            if (prime[i]) {
                primeNumbers.add(i);
            }
        }
        return primeNumbers;
    }


    public static int lowerBound(int[] a, int v){ return lowerBound(a, 0, a.length, v); }
    public static int lowerBound(int[] a, int l, int r, int v)
    {
        if(l > r || l < 0 || r > a.length)throw new IllegalArgumentException();
        int low = l-1, high = r;
        while(high-low > 1){
            int h = high+low>>>1;
            if(a[h] >= v){
                high = h;
            }else{
                low = h;
            }
        }
        return high;
    }
    public static int rlowerBound(int[] a, int v){ return lowerBound(a, 0, a.length, v); }
    public static int rlowerBound(int[] a, int l, int r, int v)
    {
        if(l > r || l < 0 || r > a.length)throw new IllegalArgumentException();
        int low = l-1, high = r;
        while(high-low > 1){
            int h = high+low>>>1;
            if(a[h] <= v){
                high = h;
            }else{
                low = h;
            }
        }
        return high;
    }
    public static long C(int n, int m)
    {
        if(m == 0 || m == n) return 1l;
        if(m > n || m < 0) return 0l;
        long res = fac[n] * quickPOW((fac[m] * fac[n - m]) % MOD, MOD - 2) % MOD;

        return res;
    }
    public static long quickPOW(long n, long m)
    {
        long ans = 1l;
        while(m > 0)
        {
            if(m % 2 == 1)
                ans = (ans * n) % MOD;
            n = (n * n) % MOD;
            m >>= 1;
        }
        return ans;
    }
    public static long quickPOW(long n, long m, long mod)
    {
        long ans = 1l;
        while(m > 0)
        {
            if(m % 2 == 1)
                ans = (ans * n) % mod;
            n = (n * n) % mod;
            m >>= 1;
        }
        return ans;
    }

    public static int gcd(int a, int b)
    {
        if(a % b == 0) return b;
        return gcd(b, a % b);
    }
    public static long gcd(long a, long b)
    {
        if(a % b == 0) return b;
        return gcd(b, a % b);
    }

    static class Randomized {
        public static void shuffle(int[] data) {
            shuffle(data, 0, data.length - 1);
        }

        public static void shuffle(int[] data, int from, int to) {
            to--;
            for (int i = from; i <= to; i++) {
                int s = nextInt(i, to);
                int tmp = data[i];
                data[i] = data[s];
                data[s] = tmp;
            }
        }

        public static void shuffle(long[] data) {
            shuffle(data, 0, data.length - 1);
        }

        public static void shuffle(long[] data, int from, int to) {
            to--;
            for (int i = from; i <= to; i++) {
                int s = nextInt(i, to);
                long tmp = data[i];
                data[i] = data[s];
                data[s] = tmp;
            }
        }

        public static int nextInt(int l, int r) {
            return RandomWrapper.INSTANCE.nextInt(l, r);
        }
    }

    static class RandomWrapper {
        private Random random;
        public static final RandomWrapper INSTANCE = new RandomWrapper(new Random());

        public RandomWrapper() {
            this(new Random());
        }

        public RandomWrapper(Random random) {
            this.random = random;
        }

        public int nextInt(int l, int r) {
            return random.nextInt(r - l + 1) + l;
        }

    }


    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        int ni() {
            return Integer.parseInt(next());
        }
        long nl() {
            return Long.parseLong(next());
        }
        double nd() {
            return Double.parseDouble(next());
        }
        String nextLine(){
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
    //--------------------------------------------------------
}