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.util.*;
import java.io.*;
 
public class Main {
    static int maxN = 1005;
    static int maxV = maxN*(maxN-1)/2;
    static ArrayList<ArrayList<Integer>> to = new ArrayList<ArrayList<Integer>>();
    static int[][] id = new int[maxN][maxN];
    public static void main(String[] args) throws Exception {
        FastScanner sc = new FastScanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int n = sc.nextInt();
        for(int i = 0; i < maxV; i++){
            to.add(new ArrayList<Integer>());
        }
        int[][] arr = new int[n][n-1];
        for(int i = 0; i < n; i++){
            for(int j = 0; j < n-1; j++){
                arr[i][j] = sc.nextInt()-1;
            }
        }
        int V = 0;
        for(int i = 0; i < n; i++){
            for(int j = 0; j < n; j++){
                if(i < j){
                    V++;
                    id[i][j] = V;
                }
            }
        }
        for(int i = 0; i < n; i++){
            for(int j = 0; j < n-1; j++){
                arr[i][j] = toId(i,arr[i][j]);
            }
            for(int j = 0; j < n-2; j++){
                to.get(arr[i][j]).add(arr[i][j+1]);
            }
        }
        int ans = 0;
        for(int i = 0; i < V; i++){
            int res = dfs(i);
            if(res == -1){
                pw.println(-1);
                pw.flush();
                return;
            }
            ans = Math.max(ans,res);
        }
        pw.println(ans);
        pw.flush();
    }
    
    private static int toId(int i, int j){
        if(i > j){
            int tmp = i;
            i = j;
            j = tmp;
        }
        return id[i][j];
    }
    
    static boolean[] visited = new boolean[maxV];
    static boolean[] calculated = new boolean[maxV];
    static int[] dp = new int[maxV];
    private static int dfs(int i){
        if(visited[i]){
            if(!calculated[i]) return -1;
            return dp[i];
        }
        dp[i] = 1;
        visited[i] = true;
        for(int next : to.get(i)){
            int res = dfs(next);
            if(res == -1) return -1;
            dp[i] = Math.max(dp[i],res+1);
        }
        calculated[i] = true;
        return dp[i];
    }

    static class GeekInteger {
        public static void save_sort(int[] array) {
            shuffle(array);
            Arrays.sort(array);
        }
 
        public static int[] shuffle(int[] array) {
            int n = array.length;
            Random random = new Random();
            for (int i = 0, j; i < n; i++) {
                j = i + random.nextInt(n - i);
                int randomElement = array[j];
                array[j] = array[i];
                array[i] = randomElement;
            }
            return array;
        }
 
    }
}

class FastScanner {
    private BufferedReader reader = null;
    private StringTokenizer tokenizer = null;
    public FastScanner(InputStream in) {
        reader = new BufferedReader(new InputStreamReader(in));
        tokenizer = null;
    }

    public String next() {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    public String nextLine() {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                return reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken("\n");
    }

    public long nextLong() {
        return Long.parseLong(next());
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public double nextDouble() {
         return Double.parseDouble(next());
    }
    
    public String[] nextArray(int n) {
        String[] a = new String[n];
        for (int i = 0; i < n; i++)
            a[i] = next();
        return a;
    }

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

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