Problem:
Score : 500 points

Problem Statement

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.

Sample Input 1

3
2 3
1 3
1 2

Sample Output 1

3

All the conditions can be satisfied if the matches are scheduled for three days as follows:

Day 1: Player 1 vs Player 2

Day 2: Player 1 vs Player 3

Day 3: Player 2 vs Player 3

This is the minimum number of days required.

Sample Input 2

4
2 3 4
1 3 4
4 1 2
3 1 2

Sample Output 2

4

All the conditions can be satisfied if the matches are scheduled for four days as follows:

Day 1: Player 1 vs Player 2, Player 3 vs Player 4

Day 2: Player 1 vs Player 3

Day 3: Player 1 vs Player 4, Player 2 vs Player 3

Day 4: Player 2 vs Player 4

This is the minimum number of days required.

Sample Input 3

3
2 3
3 1
1 2

Sample Output 3

-1

Any scheduling of the matches violates some condition.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;
import java.io.*;

class Main{
    public static void main(String[] args){
        FastScanner fsc=new FastScanner();
        int n=fsc.nextInt();
        Node[] nodes=new Node[(n*(n-1))/2];
        for(int k=0;k<nodes.length;k++) nodes[k]=new Node(k);
        for(int i=0;i<n;i++){
            int pre=-1;
            for(int j=0;j<n-1;j++){
                int k=fsc.nextInt()-1;
                int small=Math.min(i, k);
                int pl=Math.max(i, k)-(small+1);
                int st=(small*(2*n-small-1))/2;
                if(j>0){
                    nodes[pre].edges.add(st+pl);
                    nodes[st+pl].in++;
                }
                pre=st+pl;
            }
        }
        //for(Node node:nodes) for(Edge e:node.edges) System.out.println(node.id+", "+e.id);       
        fsc.close();
        int ans=shortest(nodes);
        System.out.println(ans);
    }
    static int shortest(Node[] nodes){
        int n=nodes.length;
        int ret=0;
        IntQueue zeros=new IntQueue(3*n);
        for(Node node:nodes) if(node.in==0) zeros.add(node.id);
        int num=zeros.size();
        while(zeros.size()>0){
            int size=zeros.size();
            while(size>0){
                int v=zeros.poll();
                size--;
                for(Integer u:nodes[v].edges){
                    nodes[u].in--;
                    if(nodes[u].in==0){
                        zeros.add(u);
                        num++;
                    }
                }
            }
            ret++;
        }
        if(num<n) return -1;
        return ret;
    }
    static class IntQueue{
        int[] a;
        private int max;
        int head=0, tail=0;
        private int size=0;
        public IntQueue(int max){
            this.max=max;
            a=new int[max];
        }
        public IntQueue(){
            this.max=Integer.MAX_VALUE;
            a=new int[max];
        }
        public void add(int x){
            a[tail++]=x;
            size++;
        }
        public int poll(){
            if (size == 0){
                try{throw new Exception("no elements.");}
                catch (Exception e){e.printStackTrace();}
            }
            size--;
            return a[head++];
        }
        public int size(){
            return size;
        }
        public void init(){
            tail=0;
            size=0;
        }
    }
    static class Node{
        int id;
        int in;
        ArrayList<Integer> edges;
        public Node(int id){
            this.id=id;
            edges=new ArrayList<Integer>();
            this.in=0;
        }
        @Override public boolean equals(Object o){
            if(! (o instanceof Node)) return false;
            Node n=(Node) o;
            if(n.id==id) return true;
            else return false;
        }
        @Override public int hashCode(){
            return id;
        }
    }
    static 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;
            else{
                ptr = 0;
                try{
                    buflen = in.read(buffer);
                }
                catch(IOException e){
                    e.printStackTrace();
                }
                if(buflen<=0) return false;
            }
        return true;
        }
        private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
        private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
        public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
        public String next() {
            if (!hasNext()) throw new NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while(isPrintableChar(b)) {
                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();
            while(true){
                if ('0' <= b && b <= '9') {
                    n *= 10;
                    n += b - '0';
                }
                else if(b == -1 || !isPrintableChar(b)) return minus ? -n : n;
                else throw new NumberFormatException();
                b = readByte();
            }
        }
        public int nextInt() {
            long nl = nextLong();
            if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
            return (int) nl;
        }
        public double nextDouble() { return Double.parseDouble(next());}
        public void close(){
            try{in.close();}
            catch(IOException e){e.printStackTrace();}
        }
    }
}