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)

/*
 _____ ____ _____   ___   ___  __  ___  
|_   _/ __ \_   _| |__ \ / _ \/_ |/ _ \ 
  | || |  | || |      ) | | | || | (_) |
  | || |  | || |     / /| | | || |\__, |
 _| || |__| || |_   / /_| |_| || |  / / 
|_____\____/_____| |____|\___/ |_| /_/   
*/
#include <bits/stdc++.h>
#define rep(i, a, b) for (int i = (a); i < (b); i++)
#define per(i, a, b) for (long long i = (a); i > (b); i--)
#define a(x) (x.begin(), x.end())
#define ar(x) (x.rbegin(), x.rend())
#define pb push_back
#define Pb() pop_back()
#define ll long long int
#define ull unsigned long long int
#define pii pair<int, int>
#define pll pair<ll, ll>
#define sc scanf
#define scin(x) sc("%d", &(x))
#define scln(x) sc("%lld", &(x))
#define pf prllf
#define ms(a, b) memset(a, b, sizeof(a))
#define mp make_pair
#define db double
#define EPS 10E-10
#define ff first
#define ss second
#define sqr(x) (x) * (x)
#define vi vector<int>
#define vl vector<ll>
#define vii vector<vector<int>>
#define vll vector<vector<ll>>
#define DBG pf("HI\n")
#define MOD 1000000007
#define CIN                       \
    ios_base::sync_with_stdio(0); \
    cin.tie(0);                   \
    cout.tie(0)
#define RUN_CASE(t, T) for (__typeof(t) t = 1; t <= T; t++)
#define CASE(t) prllf("Case %d: ", t)
#define CASEL(t) prllf("Case %d:\n", t)
#define intlimit 2147483647
#define longlimit 9223372036854775807
#define infinity (1 << 28)
#define gcd(a, b) __gcd(a, b)
#define lcm(a, b) ((a) * (b) / gcd(a, b))
#define PI 2 * acos(0.0)
using namespace std;
int main()
{
    CIN;
    int n;
    cin >> n;
    vii v(n,vi(n-1));
    rep(i,0,n)
    rep(j,0,n-1)
    cin >> v[i][j];
    vi last(n,0);
    int coco = 0;
    while(1){
        set<int>s;
        rep(i,0,n){
            if(last[i]>=n-1)continue;
            int b = v[i][last[i]]-1;
            if(v[b][last[b]]==i+1&&!s.count(i)&&!s.count(b)){
                last[i]++;
                last[b]++;
                s.insert(i);
                s.insert(b);
            }
        }
        coco++;
        int sos = 0;
        rep(i,0,n){
            if(last[i]<n-1){
                sos++;
            }
            //cout << last[i] << " ";
        }
        //cout << endl;
        if(!sos)
        break;
        if(s.size()==0){
            cout << -1;
            return 0;
        }
    }
    cout << coco;
}