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.Arrays;
import java.util.NoSuchElementException;
import java.util.PrimitiveIterator;
import java.util.function.IntBinaryOperator;
import java.util.function.IntFunction;
import java.util.function.IntPredicate;
import java.util.function.IntUnaryOperator;
import java.util.function.LongUnaryOperator;
import static java.lang.Math.max;
import static java.lang.Math.min;



public class Main {
    public static void main(String[] args) {
        StringBuilder out = new StringBuilder();
        solve(out);
        PrintWriter pw = new PrintWriter(System.out);
        pw.println(out);
        pw.flush();
        pw.close();
    }

    public static void solve(StringBuilder out) {
        int n = In.ni();
        IntArrayList[] g = new IntArrayList[n * n];
        for (int i = 0; i < n * n; i++) {
            g[i] = new IntArrayList();
        }
        int[] in = new int[n * n];
        for (int i = 0; i < n; i++) {
            int u = In.ni() - 1;
            int from = min(i, u) * n + max(i, u);
            for (int j = 1; j < n - 1; j++) {
                int v = In.ni() - 1;
                int to = min(i, v) * n + max(i, v);
                g[from].add(to);
                in[to]++;
                // Debug: {
                //     int fu = from / n + 1;
                //     int fv = from % n + 1;
                //     int tu = to / n + 1;
                //     int tv = to % n + 1;
                //     out.append(String.format("(%d, %d) -> (%d, %d)\n", fu, fv, tu, tv));
                // }
                from = to;
            }
        }

        IntQueue q = new IntQueue(n * n);
        for (int i = 0; i < n; i++) {
            for (int j = i + 1; j < n; j++) {
                if (in[i * n + j] == 0) {
                    q.add(i * n + j);
                }
            }
        }

        int cnt = 0;
        int ans = 0;
        while (q.size() > 0) {
            int sz = q.size();
            cnt += sz;
            while (sz --> 0) {
                int u = q.poll();
                g[u].iterator().forEachRemaining((int v) -> {
                    in[v]--;
                    if (in[v] == 0) {
                        q.add(v);
                    }
                });
            }
            ans++;
        }
        if (cnt != n * (n - 1) / 2) {
            out.append(-1);
        } else {
            out.append(ans);
        }
    }
}


/**
 * @author https://atcoder.jp/users/suisen
 */
final class In {
    public static final FastScanner fsc = new FastScanner();
    public static int ni() {return fsc.nextInt();}
    public static int[] ni(final int n) {
        final int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = fsc.nextInt();
        return a;
    }
    public static int[] ni(final int n, final IntUnaryOperator f) {
        final int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = f.applyAsInt(fsc.nextInt());
        return a;
    }
    public static int[][] ni(final int n, final int m) {
        final int[][] a = new int[n][m];
        for (int i = 0; i < n; i++) a[i] = ni(m);
        return a;
    }
    public static int[][] ni(final int n, final int m, final IntUnaryOperator f) {
        final int[][] a = new int[n][m];
        for (int i = 0; i < n; i++) a[i] = ni(m, f);
        return a;
    }
    public static long nl() {return fsc.nextLong();}
    public static long[] nl(final int n) {
        final long[] a = new long[n];
        for (int i = 0; i < n; i++) a[i] = fsc.nextLong();
        return a;
    }
    public static long[] nl(final int n, final LongUnaryOperator f) {
        final long[] a = new long[n];
        for (int i = 0; i < n; i++) a[i] = f.applyAsLong(fsc.nextLong());
        return a;
    }
    public static long[][] nl(final int n, final int m) {
        final long[][] a = new long[n][m];
        for (int i = 0; i < n; i++) a[i] = nl(m);
        return a;
    }
    public static long[][] nl(final int n, final int m, final LongUnaryOperator f) {
        final long[][] a = new long[n][m];
        for (int i = 0; i < n; i++) a[i] = nl(m, f);
        return a;
    }
    public static char[] nc() {return fsc.next().toCharArray();}
    public static char[][] nc(final int n) {
        final char[][] c = new char[n][];
        for (int i = 0; i < n; i++) c[i] = nc();
        return c;
    }
    public static double nd() {return fsc.nextDouble();}
    public static double[] nd(final int n) {
        final double[] a = new double[n];
        for (int i = 0; i < n; i++) a[i] = fsc.nextDouble();
        return a;
    }
    public static double[][] nd(final int n, final int m) {
        final double[][] a = new double[n][m];
        for (int i = 0; i < n; i++) a[i] = nd(m);
        return a;
    }
    public static String ns() {return fsc.next();}
    public static String[] ns(final int n) {
        final String[] s = new String[n];
        for (int i = 0; i < n; i++) s[i] = fsc.next();
        return s;
    }
    public static boolean[][] grid(final int h, final int w, final char trueCharacter) {
        final boolean[][] grid = new boolean[h][w];
        for (int i = 0; i < h; i++) {
            final char[] s = fsc.next().toCharArray();
            for (int j = 0; j < w; j++) grid[i][j] = s[j] == trueCharacter;
        }
        return grid;
    }
}


final class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    private boolean hasNextByte() {
        if (ptr < buflen) return true;
        ptr = 0;
        try {buflen = in.read(buffer);}
        catch (final IOException e) {e.printStackTrace();}
        return buflen > 0;
    }
    private int readByte() {return hasNextByte() ? buffer[ptr++] : -1;}
    public boolean hasNext() {
        while (hasNextByte() && !(33 <= buffer[ptr] && buffer[ptr] <= 126)) ptr++;
        return hasNextByte();
    }
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        final StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (33 <= b && b <= 126) {sb.appendCodePoint(b); b = readByte();}
        return sb.toString();
    }
    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {minus = true; b = readByte();}
        if (b < '0' || '9' < b) throw new NumberFormatException();
        for (; ; b = readByte()) {
            if ('0' <= b && b <= '9') n = n * 10 + b - '0';
            else if (b == -1 || !(33 <= b && b <= 126)) return minus ? -n : n;
            else throw new NumberFormatException();
        }
    }
    public int nextInt() {return Math.toIntExact(nextLong());}
    public double nextDouble() {return Double.parseDouble(next());}
}



/**
 * @author https://atcoder.jp/users/suisen
 */
final class IntArrayList implements Iterable<Integer> {
    private int[] a;
    private int tail = 0;
    private static final int DEFAULT_SIZE = 64;
    public IntArrayList(final int capacity) {this.a = new int[Math.max(1, capacity)];}
    public IntArrayList() {this(DEFAULT_SIZE);}
    public void add(final int v) {
        if (tail == a.length) grow();
        a[tail++] = v;
    }
    public int removeLast() {return a[tail--];}
    public int get(final int i) {
        if (i >= tail) throw new IndexOutOfBoundsException("Index " + i + " out of bounds for length " + size());
        return a[i];
    }
    public void set(final int i, final int v) {
        if (i >= tail) throw new IndexOutOfBoundsException("Index " + i + " out of bounds for length " + size());
        a[i] = v;
    }
    private void grow() {
        final int[] b = new int[a.length << 1];
        System.arraycopy(a, 0, b, 0, a.length);
        a = b;
    }
    public int size() {return tail;}
    public void reverse(final int begin, final int end) {IntArrays.reverse(a, begin, end);}
    public void reverse() {IntArrays.reverse(a, 0, tail);}
    public int[] toArray() {
        final int[] ret = new int[tail];
        System.arraycopy(a, 0, ret, 0, tail);
        return ret;
    }
    public boolean addIf(final int v, final IntPredicate p) {
        if (p.test(v)) {add(v); return true;}
        return false;
    }
    public void clear() {tail = 0;}
    public PrimitiveIterator.OfInt iterator() {return new IntArrayListIterator();}
    private class IntArrayListIterator implements PrimitiveIterator.OfInt {
        private int i = 0;
        public boolean hasNext() {return i < tail;}
        public int nextInt() {return a[i++];}
    }
}


/**
 * @author https://atcoder.jp/users/suisen
 * 
 * 1. DESTRUCTIVE methods for int arrays.
 * 2. methods that receives arrays and return some results (except for int arrays).
 */
final class IntArrays {
    private IntArrays(){}
    public static void swap(final int[] a, final int u, final int v) {
        final int tmp = a[u]; a[u] = a[v]; a[v] = tmp;
    }
    public static void reverse(final int[] a, final int begin, final int end) {
        for (int i = begin; i < begin + (end - begin) / 2; i++) swap(a, i, begin + end - i - 1);
    }
    public static void reverse(final int[] a) {reverse(a, 0, a.length);}
    public static void sortDescending(final int[] a) {Arrays.sort(a); reverse(a);}
    public static int reduce(final int[] a, final IntBinaryOperator op) {
        int ret = a[0]; for (int i = 1; i < a.length; i++) ret = op.applyAsInt(ret, a[i]);
        return ret;
    }
    public static void map(final int[] a, final IntUnaryOperator op) {Arrays.setAll(a, i -> op.applyAsInt(a[i]));}
    public static int filter(final int[] src, final int[] dst, final IntPredicate p) {
        int idx = 0;
        for (final int e : src) if (p.test(e)) dst[idx++] = e;
        return idx;
    }
    public static int filterIndex(final int[] dst, final int beginIndex, final int endIndex, final IntPredicate p) {
        int idx = 0;
        for (int i = beginIndex; i < endIndex; i++) if (p.test(i)) dst[idx++] = i;
        return idx;
    }
    public static int filterIndex(final int dst[], final int endIndex, final IntPredicate p) {
        return filterIndex(dst, 0, endIndex, p);
    }
    public static void accumulate(final int[] a, final IntBinaryOperator op) {
        for (int i = 1; i < a.length; i++) a[i] = op.applyAsInt(a[i - 1], a[i]);
    }
    public static void accumulate(final int[] a) {
        for (int i = 1; i < a.length; i++) a[i] += a[i - 1];
    }
    public static void permute(int[] a, int[] p) {
        int n = p.length;
        boolean[] settled = new boolean[n];
        for (int i = 0; i < n; i++) {
            for (int j = i; !settled[j]; j = p[j]) {
                if (p[j] == i) {
                    settled[j] = true;
                    break;
                }
                swap(a, j, p[j]);
                settled[j] = true;
            }
        }
    }
    public static int compare(final int[] a, final int[] b) {
        for (int i = 0; i < a.length; i++) {
            if (i >= b.length) return -1;
            if (a[i] > b[i]) return 1;
            if (a[i] < b[i]) return -1;
        }
        return a.length < b.length ? 1 : 0;
    }
    public static boolean equals(final int[] a, final int[] b) {return compare(a, b) == 0;}
    public static String join(final int[] a, final String sep) {
        final StringBuilder sb = new StringBuilder();
        for (int i = 0; i < a.length; i++) {
            sb.append(a[i]);
            if (i < a.length - 1) sb.append(sep);
        }
        return sb.toString();
    }
    public static String joinWithPrefixAndSuffix(final int[] a, final IntFunction<String> idxToPre, final IntFunction<String> idxToSuf, final String sep) {
        final StringBuilder sb = new StringBuilder();
        for (int i = 0; i < a.length; i++) {
            sb.append(idxToPre.apply(i)).append(a[i]).append(idxToSuf.apply(i));
            if (i < a.length - 1) sb.append(sep);
        }
        return sb.toString();
    }
}


/**
 * @author https://atcoder.jp/users/suisen
 * 
 * Queue for int type.
 */
final class IntQueue implements Iterable<Integer> {
    private static final int DEFAULT_SIZE = 64;
    private int[] q;
    private int head = 0, tail = 0;
    public IntQueue(final int capacity) {this.q = new int[capacity];}
    public IntQueue() {this(DEFAULT_SIZE);}
    public int peek() {
        if (head == tail) throw new NoSuchElementException("No Elements.");
        return q[head];
    }
    public int getFromHead(int index) {
        if (head + index >= tail || index < 0) throw new NoSuchElementException("Index out of bounds.");
        return q[head + index];
    }
    public int getFromTail(int index) {
        if (head + index >= tail || index < 0) throw new NoSuchElementException("Index out of bounds.");
        return q[tail - 1 - index];
    }
    public void add(final int v) {
        if (tail == q.length) grow();
        q[tail++] = v;
    }
    public void add(final int... vals) {for (int v : vals) add(v);}
    public int poll() {
        if (head == tail) throw new NoSuchElementException("No Elements.");
        int ret = q[head++];
        if (head == tail) head = tail = 0;
        else if (head >= 1e7) relocate();
        return ret;
    }
    private void relocate() {
        final int[] newQ = new int[q.length];
        System.arraycopy(q, head, newQ, 0, tail - head);
        q = newQ;
        tail -= head;
        head = 0;
    }
    public int size() {return tail - head;}
    public void clear() {head = tail = 0;}
    private void grow() {
        final int[] grown = new int[q.length << 1];
        final int len = size();
        System.arraycopy(q, head, grown, 0, len);
        q = grown;
        tail = len;
        head = 0;
    }
    public PrimitiveIterator.OfInt iterator() {return new IntQueueIterator();}
    private class IntQueueIterator implements PrimitiveIterator.OfInt {
        private int i = head;
        public boolean hasNext() {return i < tail;}
        public int nextInt() {return q[i++];}
    }
}
