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: Time Limit Exceeded)

// Charan Sriramula

#include<bits/stdc++.h>
using namespace std;
typedef long double ld;
typedef long long int ll;

const ll logx=30;
const ll N=1e6+5;
const ll M=1e3+5;
const ll mod=998244353;
const ll INF=1e18+5;
const double PI = 3.14159265358979323846;

#define ints(n) scanf("%d",&n)
#define intp(n) printf("%d\n",n)
#define longs(n) scanf("%intd",&n)
#define longp(n) printf("%intd\n",n)

inline ll mul(ll a, ll b,ll p){ return (a * 1ll * b) % p; }
inline ll sub(ll a, ll b,ll p){ ll c = a - b; if(c < 0) c += p; return c; }
inline ll add(ll a, ll b,ll p){ ll c = a + b; if(c > p) c -= p; return c; }

#define f first
#define s second
#define pb(x) push_back(x)
#define pf(x) push_front(x)
#define mp(x,y) make_pair(x,y)
#define GCD(a,b) __gcd((a),(b))
#define all(v) v.begin(),v.end()
#define bits(x) __builtin_popcountll(x)
#define LCM(a,b) ((a)*(b))/GCD((a),(b))
#define ms(dp,val) memset(dp,val,sizeof(dp))
#define fast ios_base::sync_with_stdio(false);cin.tie(NULL);
template<typename T> T power(T x,T y,ll m){T ans=1;while(y>0){if(y&1LL) ans=(ans*x)%m;y>>=1ll;x=(x*x)%m;}return ans%m;}

#define trace1(x)                cerr<<#x<<": "<<x<<endl
#define trace2(x, y)             cerr<<#x<<": "<<x<<" | "<<#y<<": "<<y<<endl
#define trace3(x, y, z)          cerr<<#x<<":" <<x<<" | "<<#y<<": "<<y<<" | "<<#z<<": "<<z<<endl
#define trace4(a, b, c, d)       cerr<<#a<<": "<<a<<" | "<<#b<<": "<<b<<" | "<<#c<<": "<<c<<" | "<<#d<<": "<<d<<endl
#define trace5(a, b, c, d, e)    cerr<<#a<<": "<<a<<" | "<<#b<<": "<<b<<" | "<<#c<<": "<<c<<" | "<<#d<<": "<<d<<" | "<<#e<< ": "<<e<<endl
#define trace6(a, b, c, d, e, f) cerr<<#a<<": "<<a<<" | "<<#b<<": "<<b<<" | "<<#c<<": "<<c<<" | "<<#d<<": "<<d<<" | "<<#e<< ": "<<e<<" | "<<#f<<": "<<f<<endl

ll n,vis[N];
deque<ll> v[N];

int main()
{
  cin>>n;
  ll day=0;
  set<ll> idx;
  for(ll i=1;i<=n;i++)
  {
    idx.insert(i);
    for(ll j=1;j<n;j++)
    {
      ll x;
      cin>>x;
      v[i].pb(x);
    }
  }
  while(1)
  {
    day++;
    //trace1(day);
    ll ff=0,in=0;
    set<ll> temp;
    for(auto i:idx){vis[i]=0;}
    for(auto i:idx)
    {
      if(v[i].size()==0||vis[i]){continue;}
      ll cur=i,nex=v[i].front();
      if(vis[nex]){continue;}
      if(v[nex].front()==cur)
      {
        in++;
        vis[i]=1;
        vis[nex]=1;
        //cout<<i<<" "<<nex<<endl;
        v[i].pop_front();
        v[nex].pop_front();
        if(v[i].size()==0){temp.insert(i);}
        if(v[nex].size()==0){temp.insert(nex);}
      }
    }
    //cout<<endl;
    for(auto j:temp){idx.erase(j);}
    //for(ll i=1;i<=n;i++)
    //{
      if(idx.size()){ff=1;}
    //}
    //if(in==0){cout<<-1<<endl;exit(0);}
    if(day>N||in==0){cout<<-1<<endl;exit(0);}
    if(ff){continue;}
    break;
  }
  cout<<day<<endl;
}