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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.LinkedList;
import java.util.NoSuchElementException;
import java.util.StringJoiner;

class Main {

    static PrintWriter out;
    static InputReader sc;

    static ArrayList<LinkedList<Integer>> a;
    static HashSet<Pair> q = new HashSet<>();

    public static void main(String[] args) {
        sc = new InputReader(System.in);
        out = new PrintWriter(System.out);
        solve();
        out.flush();
    }

    static void solve() {
        int N = sc.nextInt();
        a = new ArrayList<>();
        for (int i = 0; i < N; i++) {
            a.add(new LinkedList<>());
            for (int j = 0; j < N - 1; j++) {
                a.get(i).add(sc.nextInt() - 1);
            }
            Collections.reverse(a.get(i));
        }
        for (int i = 0; i < N; i++) {
            check(i);
        }
        int day = 0;
        while (q.size() > 0) {
            day++;
            HashSet<Pair> preQ = new HashSet<>();
            HashSet<Pair> tmp = new HashSet<>();
            tmp = q;
            q = preQ;
            preQ = tmp;
            for (Pair pair : preQ) {
                int i = pair.first, j = pair.second;
                a.get(i).pollLast();
                a.get(j).pollLast();
            }
            for (Pair pair : preQ) {
                int i = pair.first, j = pair.second;
                check(i);
                check(j);
            }
        }
        for (LinkedList<Integer> list : a) {
            if (list.size() != 0) {
                out.println(-1);
                return;
            }
        }
        out.println(day);
    }

    static void check(int i) {
        if (a.get(i).size() == 0) {
            return;
        }
        int j = a.get(i).getLast();
        if (a.get(j).size() == 0) {
            return;
        }
        if (a.get(j).getLast() == i) {
            if (i > j) {
                int tmp = i;
                i = j;
                j = tmp;
            }
            q.add(new Pair(i, j));
        }
    }

    /**
     * C++のPairと同じ
     */
    public static class Pair implements Comparable<Pair> {
        int first;
        int second;

        public Pair(int first, int second) {
            this.first = first;
            this.second = second;
        }

        @Override
        public int hashCode() {
            return Integer.valueOf(this.first + this.second).hashCode();
        }

        @Override
        public boolean equals(Object obj) {
            if (this == obj) {
                return true;
            }
            if (!(obj instanceof Pair)) {
                return false;
            }
            Pair pair = (Pair) obj;
            return this.first == pair.first && this.second == pair.second;
        }

        @Override
        public int compareTo(Pair o) {
            return Integer.compare(this.first, o.first);
        }

        @Override
        public String toString() {
            return String.format("%d %d", this.first, this.second);
        }

    }

    static void debug(Object... args) {
        StringJoiner j = new StringJoiner(" ");
        for (Object arg : args) {
            if (arg == null) {
                j.add("null");
            } else if (arg instanceof int[]) {
                j.add(Arrays.toString((int[]) arg));
            } else if (arg instanceof long[]) {
                j.add(Arrays.toString((long[]) arg));
            } else if (arg instanceof double[]) {
                j.add(Arrays.toString((double[]) arg));
            } else if (arg instanceof char[]) {
                j.add(Arrays.toString((char[]) arg));
            } else if (arg instanceof boolean[]) {
                j.add(Arrays.toString((boolean[]) arg));
            } else if (arg instanceof Object[]) {
                j.add(Arrays.toString((Object[]) arg));
            } else {
                j.add(arg.toString());
            }
        }
        System.err.println(j.toString());
    }

    static class InputReader {

        private InputStream in;
        private byte[] buffer = new byte[1024];
        private int curbuf;
        private int lenbuf;

        public InputReader(InputStream in) {
            this.in = in;
            this.curbuf = this.lenbuf = 0;
        }

        public boolean hasNextByte() {
            if (this.curbuf >= this.lenbuf) {
                this.curbuf = 0;
                try {
                    this.lenbuf = this.in.read(this.buffer);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (this.lenbuf <= 0) {
                    return false;
                }
            }
            return true;
        }

        private int readByte() {
            if (this.hasNextByte()) {
                return this.buffer[this.curbuf++];
            } else {
                return -1;
            }
        }

        private boolean isSpaceChar(int c) {
            return !(c >= 33 && c <= 126);
        }

        private void skip() {
            while (this.hasNextByte() && this.isSpaceChar(this.buffer[this.curbuf])) {
                this.curbuf++;
            }
        }

        public boolean hasNext() {
            this.skip();
            return this.hasNextByte();
        }

        public String next() {
            if (!this.hasNext()) {
                throw new NoSuchElementException();
            }
            StringBuilder sb = new StringBuilder();
            int b = this.readByte();
            while (!this.isSpaceChar(b)) {
                sb.appendCodePoint(b);
                b = this.readByte();
            }
            return sb.toString();
        }

        public int nextInt() {
            if (!this.hasNext()) {
                throw new NoSuchElementException();
            }
            int c = this.readByte();
            while (this.isSpaceChar(c)) {
                c = this.readByte();
            }
            boolean minus = false;
            if (c == '-') {
                minus = true;
                c = this.readByte();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res = res * 10 + c - '0';
                c = this.readByte();
            } while (!this.isSpaceChar(c));
            return minus ? -res : res;
        }

        public long nextLong() {
            if (!this.hasNext()) {
                throw new NoSuchElementException();
            }
            int c = this.readByte();
            while (this.isSpaceChar(c)) {
                c = this.readByte();
            }
            boolean minus = false;
            if (c == '-') {
                minus = true;
                c = this.readByte();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res = res * 10 + c - '0';
                c = this.readByte();
            } while (!this.isSpaceChar(c));
            return minus ? -res : res;
        }

        public double nextDouble() {
            return Double.parseDouble(this.next());
        }

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

        public long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = this.nextLong();
            }
            return a;
        }

        public char[][] nextCharMap(int n, int m) {
            char[][] map = new char[n][m];
            for (int i = 0; i < n; i++) {
                map[i] = this.next().toCharArray();
            }
            return map;
        }
    }
}