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.*; import java.math.*;
public class Main{
	//Don't have to see. start------------------------------------------
	static class InputIterator{
		ArrayList<String> inputLine = new ArrayList<String>(1024);
		int index = 0; int max; String read;
		InputIterator(){
			BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
			try{
				while((read = br.readLine()) != null){
					inputLine.add(read);
				}
			}catch(IOException e){}
			max = inputLine.size();
		}
		boolean hasNext(){return (index < max);}
		String next(){
			if(hasNext()){
				return inputLine.get(index++);
			}else{
				throw new IndexOutOfBoundsException("There is no more input");
			}
		}
	}
	static HashMap<Integer, String> CONVSTR = new HashMap<Integer, String>();
	static InputIterator ii = new InputIterator();//This class cannot be used in reactive problem.
	static PrintWriter out = new PrintWriter(System.out);
	static void flush(){out.flush();}
	static void myout(Object t){out.println(t);}
	static void myerr(Object t){System.err.print("debug:");System.err.println(t);}
	static String next(){return ii.next();}
	static boolean hasNext(){return ii.hasNext();}
	static int nextInt(){return Integer.parseInt(next());}
	static long nextLong(){return Long.parseLong(next());}
	static double nextDouble(){return Double.parseDouble(next());}
	static ArrayList<String> nextStrArray(){return myconv(next(), 8);}
	static ArrayList<String> nextCharArray(){return myconv(next(), 0);}
	static ArrayList<Integer> nextIntArray(){
		ArrayList<String> input = nextStrArray(); ArrayList<Integer> ret = new ArrayList<Integer>(input.size());
		for(int i = 0; i < input.size(); i++){
			ret.add(Integer.parseInt(input.get(i)));
		}
		return ret;
	}
	static ArrayList<Long> nextLongArray(){
		ArrayList<String> input = nextStrArray(); ArrayList<Long> ret = new ArrayList<Long>(input.size());
		for(int i = 0; i < input.size(); i++){
			ret.add(Long.parseLong(input.get(i)));
		}
		return ret;
	}
	static String myconv(Object list, int no){//only join
		String joinString = CONVSTR.get(no);
		if(list instanceof String[]){
			return String.join(joinString, (String[])list);
		}else if(list instanceof ArrayList){
			return String.join(joinString, (ArrayList)list);
		}else{
			throw new ClassCastException("Don't join");
		}
	}
	static ArrayList<String> myconv(String str, int no){//only split
		String splitString = CONVSTR.get(no);
		return new ArrayList<String>(Arrays.asList(str.split(splitString)));
	}
	public static void main(String[] args){
		CONVSTR.put(8, " "); CONVSTR.put(9, "\n"); CONVSTR.put(0, "");
		solve();flush();
	}
	//Don't have to see. end------------------------------------------
	static ArrayDeque<String> queue = new ArrayDeque<String>();
	static Node[] list;
	static int N;
	static void solve(){//Here is the main function
		N = nextInt();
		list = new Node[N];
		for(int i = 0; i < N; i++){
			ArrayList<Integer> tmp = nextIntArray();
			int[] add = new int[N - 1];
			for(int j = 0; j < N - 1; j++){
				add[j] = tmp.get(j) - 1;
			}
			list[i] = new Node(add);
		}
		int output = 0;
		for(int i = 0; i < N; i++){
			check(i);
		}
		while(queue.size() > 0){
			ArrayDeque<String> tmpQueue = (ArrayDeque<String>)queue.clone();
			queue = new ArrayDeque<String>();
			output++;
			while(tmpQueue.size() > 0){
				String tmp = tmpQueue.pollFirst();
				int L = Integer.parseInt(tmp.split(":")[0]);
				int R = Integer.parseInt(tmp.split(":")[1]);
				list[L].lastIndex++;
				list[R].lastIndex++;
				check(L);
				check(R);
			}
		}
		for(int i = 0; i < N; i++){
			if(list[i].lastIndex != N - 1){
				output = -1;
			}
		}
		myout(output);
	}
	//Method addition frame start

static class Node{
	int[] next;
	int lastIndex = 0;
	Node(int[] n){
		next = n;
	}
}

static void check(int left){
	if(list[left].lastIndex == N - 1){
		return;
	}
	int right = list[left].next[list[left].lastIndex];
	if(list[right].lastIndex == N - 1){
		return;
	}
	if(list[right].next[list[right].lastIndex] == left){
		if(right < left){
			int tmp = left;
			left = right;
			right = tmp;
		}
		if(!queue.contains(left + ":" + right)){
			String add = left + ":" + right;
			queue.addLast(add);
		}
	}
}

	//Method addition frame end
}
