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.*;
import java.util.*;
import java.math.*;
// import java.awt.Point;
 
public class Main {
    InputStream is;
    PrintWriter out;
    String INPUT = "";
 
    static int mod = 1_000_000_007;
    // int mod = 998244353;
    // long inf = Long.MAX_VALUE/2;
    int inf = Integer.MAX_VALUE/2;
    int val = 0;

    void solve(){
        int n = ni();
        int[][] a = new int[n][n-1];
        int total = n*n;
        ArrayList[] edge = new ArrayList[total];
        int[] order = new int[total];
        Arrays.fill(order,-1);
        for(int i = 0; i < total; i++){
            edge[i] = new ArrayList<Integer>();
        }
        for(int i = 0; i < n; i++){
            int prev = -1;
            for(int j = 0; j < n-1; j++){
                a[i][j] = ni()-1;
                int node =  Math.min(i,a[i][j])*n+Math.max(i,a[i][j]);
                if(order[node]==-1) order[node] = 0;
                // out.println(node);
                if(prev==-1){
                    prev = node;
                    continue;
                }
                edge[prev].add(node);
                order[node]++;
                // System.err.println(prev+" "+node);
                prev = node;
            }
        }
        int[] res = sortTopological(edge,order,n*n, n);
        if(res.length!=n*(n-1)/2){
            out.println(-1);
            return;
        }
        out.println(val);
        // for(int i = 0; i < res.length; i++){
        //     out.println(res[i]);
        // }
        // out.println(res-(n*n-n*(n-1)/2));
        // for(int i : res){
        //     int c = i/n;
        //     int d = i%n;
        //     out.println(c+" "+d);
        // }
    }

    int[] sortTopological(ArrayList<Integer>[] outer, int[] order, int n, int m){
        Deque<Integer> st = new ArrayDeque<>();
        Deque<Integer> nst = new ArrayDeque<>();
        for(int i = 0; i < n; i++){
            if(order[i]==0){
                st.add(i);
            }
        }
        ArrayList<Integer> ans = new ArrayList<>();
        int ret = 0;
        int prev = -1;
        while(true){
            HashMap<Integer,Integer> map = new HashMap<>();
            while(!st.isEmpty()){
                int cur = st.pop();
                ans.add(cur);
                for(int i : outer[cur]){
                    order[i]--;
                    if(order[i]==0){
                        nst.push(i);
                    }
                }
                int a = cur/m;
                int b = cur%m;
                map.put(a, map.getOrDefault(a,0)+1);
                map.put(b, map.getOrDefault(b,0)+1);
                // System.err.println(a+" "+b);
            }

            

            int ma = 0;
            for(int i : map.keySet()){
                ma = Math.max(ma, map.get(i));
            }

            ret += ma;
            // System.err.println("ret "+ret);

            if(nst.isEmpty()) break;
            
            while(!nst.isEmpty()){
                int cur = nst.pop();
                st.push(cur);
            }
        }
        int[] res = new int[ans.size()];
        for(int i = 0; i < ans.size(); i++){
            res[i] = ans.get(i);
        }
        // System.err.println(ret);
        val = ret;

        return res;
    }

    void run() throws Exception
    {
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);
        long s = System.currentTimeMillis();
        solve();
        out.flush();
        if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
    }
    
    public static void main(String[] args) throws Exception { new Main().run(); }
    
    private byte[] inbuf = new byte[1024];
    private int lenbuf = 0, ptrbuf = 0;
    
    private int readByte()
    {
        if(lenbuf == -1)throw new InputMismatchException();
        if(ptrbuf >= lenbuf){
            ptrbuf = 0;
            try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
            if(lenbuf <= 0)return -1;
        }
        return inbuf[ptrbuf++];
    }
    
    private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
    private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
    
    private double nd() { return Double.parseDouble(ns()); }
    private char nc() { return (char)skip(); }
    
    private String ns()
    {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while(!(isSpaceChar(b) && b != ' ')){
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    
    private char[] ns(int n)
    {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while(p < n && !(isSpaceChar(b))){
            buf[p++] = (char)b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }
    
    private char[][] nm(int n, int m)
    {
        char[][] map = new char[n][];
        for(int i = 0;i < n;i++)map[i] = ns(m);
        return map;
    }
    
    private int[] na(int n)
    {
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = ni();
        return a;
    }
    
    private int ni()
    {
        int num = 0, b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private long nl()
    {
        long num = 0;
        int b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); }
 
}
