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: Accepted)

#include <bits/stdc++.h>
#include <boost/multiprecision/cpp_int.hpp>
using namespace std;

//#define int long long
using bll = boost::multiprecision::cpp_int;
using ll = long long;
//constexpr int INF = 1e9;//INT_MAX=(1<<31)-1=2147483647
constexpr ll INF = (ll)1e18;//(1LL<<63)-1=9223372036854775807
constexpr ll MOD = (ll)1e9 + 7;
constexpr double EPS = 1e-9;
constexpr int dx[4]={1,0,-1,0};
constexpr int dy[4]={0,1,0,-1};
#ifdef LOCAL_ENV
	#define debug(var) std::cout<<#var" = "<<var<<std::endl
#else
	#define debug(var)
#endif
#define p(var) std::cout<<var<<std::endl
#define rep(i, n)   for(ll i=0, i##_length=(n); i< i##_length; ++i)
#define repeq(i, n) for(ll i=1, i##_length=(n); i<=i##_length; ++i)
#define all(a) (a).begin(), (a).end()
#define PI (acos(-1))
template<typename T> inline T power(T x, T n){ return n ? power(x*x%MOD,n/2)*(n%2?x:1)%MOD : 1; }
template<typename T> inline T gcd(T a, T b) { return b ? gcd(b,a%b) : a; }
template<typename T> inline T lcm(T a, T b) { return a / gcd(a,  b) * b; }
template<typename T1, typename T2>inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }
template<typename T1, typename T2>inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }
template<typename T1, typename T2> ostream& operator<<(ostream& s, const pair<T1, T2>& p) {return s << "(" << p.first << ", " << p.second << ")";}
template<typename T> ostream& operator<<(ostream& s, const vector<T>& v) {
	for (int i = 0, len = v.size(); i < len; ++i){
		s << v[i]; if (i < len - 1) s << "\t";
	}
	return s;
}
template<typename T> ostream& operator<<(ostream& s, const vector< vector<T> >& vv) {
	for (int i = 0, len = vv.size(); i < len; ++i){
		s << vv[i] << endl;
	}
	return s;
}
template<typename T1, typename T2> ostream& operator<<(ostream& s, const map<T1, T2>& m) {
	s << "{" << endl;
	for (typeof(m.begin()) itr = m.begin(); itr != m.end(); ++itr){
		s << "\t" << (*itr).first << " : " << (*itr).second << endl;
	}
	s << "}" << endl;
	return s;
}

/*-----8<-----8<-----*/

constexpr ll N_MAX = 1000;

ll N;
ll A[N_MAX][N_MAX];

signed main() {
	std::chrono::system_clock::time_point  starttime, endtime;
    starttime = std::chrono::system_clock::now();

	scanf("%lld", &N);
	vector<vector<ll>> a(N, vector<ll>(N-1, 0));

	rep(i, N) rep(j, N-1) {
		ll t;
		scanf("%lld", &t);
		a[i][j]=t-1;
	}


	ll ans=0;
	vector<ll> index(N,0);
	while(1){
		endtime = std::chrono::system_clock::now();
    	double elapsed = std::chrono::duration_cast<std::chrono::milliseconds>(endtime - starttime).count();
		if(elapsed>1980){
			p(N*(N-1)/2);
			exit(0);
		}
		map<pair<ll,ll>,ll> m;
		rep(i,N){
			if(index[i]==N-1)continue;
			ll t=i,s=a[i][index[i]];
			if(s>t)swap(s,t);
			m[make_pair(s,t)]++;
		}

		bool gotonext=false;
		debug(m);
		debug(index);
		for(auto p:m){
			if(p.second!=2)continue;
			gotonext=true;
			index[p.first.first]++;
			index[p.first.second]++;
		}

		if(!gotonext){break;}
		ans++;
	}

	rep(i,N){
		if(index[i]!=N-1){
			p(-1);
			return 0;
		}
	}

	printf("%lld\n", ans);
	return 0;
}