N players will participate in a tennis tournament. We will call them Player 1, Player 2, \ldots, Player N.

The tournament is round-robin format, and there will be N(N-1)/2 matches in total. Is it possible to schedule these matches so that all of the following conditions are satisfied? If the answer is yes, also find the minimum number of days required.

* Each player plays at most one matches in a day.
* Each player i (1 \leq i \leq N) plays one match against Player A_{i, 1}, A_{i, 2}, \ldots, A_{i, N-1} in this order.

Constraints

* 3 \leq N \leq 1000
* 1 \leq A_{i, j} \leq N
* A_{i, j} \neq i
* A_{i, 1}, A_{i, 2}, \ldots, A_{i, N-1} are all different.

Input

Input is given from Standard Input in the following format:


N
A_{1, 1} A_{1, 2} \ldots A_{1, N-1}
A_{2, 1} A_{2, 2} \ldots A_{2, N-1}
:
A_{N, 1} A_{N, 2} \ldots A_{N, N-1}


Output

If it is possible to schedule all the matches so that all of the conditions are satisfied, print the minimum number of days required; if it is impossible, print `-1`.

Examples

Input

3
2 3
1 3
1 2


Output

3


Input

4
2 3 4
1 3 4
4 1 2
3 1 2


Output

4


Input

3
2 3
3 1
1 2


Output

-1
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Vector;
import java.util.Scanner;
import java.util.Stack;
import java.util.ArrayList;

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

    static class ELeague {
        public void solve(int testNumber, Scanner in, PrintWriter out) {

            int n = in.nextInt();
            Graph g = new Graph(n * n + 1);
            int[][] match = new int[n][n - 1];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n - 1; j++) {
                    int oponent = in.nextInt();
                    int min = Math.min(i + 1, oponent);
                    int max = Math.max(i + 1, oponent);
                    match[i][j] = min * n + max;
                }
            }

        /*
        for (int i = 0; i < n; i++) {
            out.println(Arrays.toString(match[i]));
        }

         */

            // 0からほかのやつに辺を伸ばせばいい
            for (int i = 0; i < n; i++) {
                for (int j = i + 1; j < n; j++) {
                    if (match[i][0] == match[j][0]) {
                        g.addEdge(new Edge(0, match[i][0], 1));
                    }
                }
                for (int j = 1; j < n - 1; j++) {
                    g.addEdge(new Edge(match[i][j - 1], match[i][j], 1));
                }
            }


            // トポロジカルソートをする
            int[] inDeg = g.getInDeg();
            int[] dist = new int[n * n + 1];
            int cnt = 0;
            Arrays.fill(dist, 0);
            Stack<Integer> st = new Stack<>();
            st.add(0);
            while (!st.isEmpty()) {
                int now = st.pop();
                ArrayList<Edge> adj = g.getAdj()[now];
                //out.println(adj.toString());
                for (Edge e : adj) {
                    inDeg[e.to]--;
                    if (inDeg[e.to] == 0) {
                        st.add(e.to);
                        cnt++;
                    }
                    dist[e.to] = Math.max(dist[e.to], dist[e.from] + 1);
                }
            }

            //out.println(Arrays.toString(dist));
            //out.println(cnt);

            int max = -1000;
            for (int i = 0; i < dist.length; i++) {
                max = Math.max(max, dist[i]);
            }

            out.println(cnt == (n * n - n) / 2 ? max : -1);
        }

    }

    static class Graph {
        int n;
        ArrayList<Edge>[] adj;
        int[] inDeg;
        long[] vertexCost;

        public Graph(int size) {
            n = size;
            adj = new ArrayList[n];
            inDeg = new int[n];
            for (int i = 0; i < n; i++) {
                adj[i] = new ArrayList<>();
            }
            vertexCost = new long[n];
        }

        public void addEdge(Edge e) {
            adj[e.from].add(e);
            inDeg[e.to]++;
        }

        public ArrayList<Edge>[] getAdj() {
            return adj;
        }

        public int[] getInDeg() {
            return inDeg;
        }

    }

    static class Edge {
        public int from;
        public int to;
        public long cost;

        public Edge(int to) {
            this.to = to;
        }

        public Edge(int to, long cost) {
            this.to = to;
            this.cost = cost;
        }

        public Edge(int from, int to, long cost) {
            this.from = from;
            this.to = to;
            this.cost = cost;
        }

        public String toString() {
            return "Edge{" +
                    "from=" + from +
                    ", to=" + to +
                    ", cost=" + cost +
                    '}';
        }

    }
}

