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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
#define mod 1000000007
#define ll long long int
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define boost ios_base::sync_with_stdio(false);cin.tie(NULL);
#define inf 9223372036854775807
#define mini 9223372036854775807
#include <ext/pb_ds/assoc_container.hpp> 
#include <ext/pb_ds/tree_policy.hpp> 
using namespace __gnu_pbds; 
#define ordered_set tree<ll, null_type,less<ll>, rb_tree_tag,tree_order_statistics_node_update>
pair<ll,ll>s4[4]={{-1,0},{1,0},{0,-1},{0,1}};
pair<ll,ll>s8[8]={{-1,-1},{-1,0},{-1,1},{0,-1},{0,1},{1,1},{1,0},{1,-1}};
ll power(ll a,ll b)
{
	if(b==0)
		return 1;
	ll c=power(a,b/2);
	if(b%2==0)
		return ((c%mod)*(c%mod))%mod;
	else
		return ((((c%mod)*(c%mod))%mod)*a)%mod;
}
int main()
{
	boost
	ll n;
	cin>>n;
	queue<ll>q[n];
	for(ll i=0; i<n; i++)
	{
		for(ll j=0; j<n-1; j++)
		{
			ll x;
			cin>>x;
			q[i].push(x-1);
		}
	}
	ll days=0;
	for(ll i=0; i<100005; i++)
	{
		ll M[n+5];
		memset(M,0,sizeof(M));
		bool flag=false;
		for(ll j=0; j<n; j++)
		{
			if(q[j].size()>0)
			{
				if(q[q[j].front()].size()>0 && M[j]==0 && M[q[j].front()]==0 && q[q[j].front()].front()==j)
				{
					M[j]=1;
					M[q[j].front()]=1;
					q[q[j].front()].pop();
					q[j].pop();
					flag=true;
				}
			}
		}
		if(flag==true)
			days++;
	}
	for(ll i=0; i<n; i++)
	{
		//cout<<i<<" "<<q[i].size()<<endl;
		if(q[i].size()>0)
		{
			cout<<"-1"<<endl;
			return 0;
		}
	}
	cout<<days<<endl;
	return 0;
}