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.HashSet;
import java.util.Arrays;
import java.io.FilterInputStream;
import java.io.BufferedInputStream;
import java.io.InputStream;

/**
 * @author khokharnikunj8
 */

public class Main {
    public static void main(String[] args) {
        new Thread(null, new Runnable() {
            public void run() {
                new Main().solve();
            }
        }, "1", 1 << 26).start();
    }

    void solve() {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        ScanReader in = new ScanReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        ELeague solver = new ELeague();
        solver.solve(1, in, out);
        out.close();
    }

    static class ELeague {
        HashSet<Integer> set;
        int[][] ar;
        int[][] dp;
        int ans;
        int[] ptr;
        boolean flag;

        public void findIt(int node) {
            int node1 = ar[node][ptr[node]];
            if (!flag) return;
            if (set.contains(node1)) {
                flag = false;
                return;
            }
            while (ar[node1][ptr[node1]] != node) {
                set.add(node);
                findIt(node1);
                set.remove(node);
                if (!flag) return;
            }
            dp[node][ptr[node]] = Math.max(dp[node1][ptr[node1] - 1], dp[node][ptr[node] - 1]) + 1;
            dp[node1][ptr[node1]] = Math.max(dp[node1][ptr[node1] - 1], dp[node][ptr[node] - 1]) + 1;
            ans = Math.max(ans, dp[node][ptr[node]]);
            ptr[node]++;
            ptr[node1]++;
        }

        public void solve(int testNumber, ScanReader in, PrintWriter out) {
            int n = in.scanInt();
            ar = new int[n][n];
            for (int i = 0; i < n; i++) {
                for (int j = 1; j < n; j++) {
                    ar[i][j] = in.scanInt() - 1;
                }
            }
            set = new HashSet<>();
            ptr = new int[n];
            Arrays.fill(ptr, 1);
            dp = new int[n][n];
            ans = 0;
            flag = true;
            for (int i = 0; i < n; i++) {
                while (ptr[i] < n) {
                    findIt(i);
                    if (!flag) {
                        out.println(-1);
                        return;
                    }
                }
            }
            out.println(ans);

        }

    }

    static class ScanReader {
        private byte[] buf = new byte[4 * 1024];
        private int index;
        private BufferedInputStream in;
        private int total;

        public ScanReader(InputStream inputStream) {
            in = new BufferedInputStream(inputStream);
        }

        private int scan() {
            if (index >= total) {
                index = 0;
                try {
                    total = in.read(buf);
                } catch (Exception e) {
                    e.printStackTrace();
                }
                if (total <= 0) return -1;
            }
            return buf[index++];
        }

        public int scanInt() {
            int integer = 0;
            int n = scan();
            while (isWhiteSpace(n)) n = scan();
            int neg = 1;
            if (n == '-') {
                neg = -1;
                n = scan();
            }
            while (!isWhiteSpace(n)) {
                if (n >= '0' && n <= '9') {
                    integer *= 10;
                    integer += n - '0';
                    n = scan();
                }
            }
            return neg * integer;
        }

        private boolean isWhiteSpace(int n) {
            if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1) return true;
            else return false;
        }

    }
}

