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 (Clang 3.8.0) (judge verdict: Runtime Error)

#include <iostream>
#include <map>
#include <vector>
#include <algorithm>
#include <string>
#include <queue>
#include <iomanip>
#include <set>
#include <unordered_map>

#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

using namespace std;

#define rep(i,n) for(int i=0,i##_len=(n);i<i##_len;++i)
#define reps(i,n) for(int i=1,i##_len=(n);i<=i##_len;++i)
#define rrep(i,n) for(int i=((int)((n)-1));i>=0;--i)
#define rreps(i,n) for(int i=((int)(n));i>0;--i)
#define rept(n) for(int ___i___=0,i##_len=(n);___i___<i##_len;++___i___)
#define repi(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++)
#define ALL(x) (x).begin(),(x).end()
#define SZ(x) ((int)(x).size())
#define ZERO(a) memset(a,0,sizeof(a))
#define BIT(n) (1LL<<(n))
#define UNIQUE(v) v.erase(unique(v.begin(),v.end()),v.end());
#define CEIL(x, y) (((x) + (y) - 1) / (y))

// vector
template <typename T>
istream &operator>>(istream &is, vector<T> &vec) {
    for (T &x : vec) is >> x;
    return is;
}
// pair
template <typename T, typename U>
ostream &operator<<(ostream &os, pair<T, U> &pair_var) {
    os << "(" << pair_var.first << ", " << pair_var.second << ")";
    return os;
}
// vector
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &vec) {
    os << "{";
    for (int i = 0; i < vec.size(); i++) {
        os << vec[i] << (i + 1 == vec.size() ? "" : ", ");
    }
    os << "}";
    return os;
}
// map
template <typename T, typename U>
ostream &operator<<(ostream &os, map<T, U> &map_var) {
    os << "{";
    repi(itr, map_var) {
        os << *itr;
        itr++;
        if (itr != map_var.end()) os << ", ";
        itr--;
    }
    os << "}";
    return os;
}
// set
template <typename T>
ostream &operator<<(ostream &os, set<T> &set_var) {
    os << "{";
    repi(itr, set_var) {
        os << *itr;
        itr++;
        if (itr != set_var.end()) os << ", ";
        itr--;
    }
    os << "}";
    return os;
}
#define DUMPOUT cout
void dump_func() {
    DUMPOUT << endl;
}
template <class Head, class... Tail>
void dump_func(Head &&head, Tail &&... tail) {
    DUMPOUT << head;
    if (sizeof...(Tail) > 0) {
        DUMPOUT << ", ";
    }
    dump_func(std::move(tail)...);
}
#ifdef LOCAL_
#define dump(...)                                                              \
    DUMPOUT << "  " << string(#__VA_ARGS__) << ": "                            \
            << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]"        \
            << endl                                                            \
            << "    ",                                                         \
        dump_func(__VA_ARGS__)
#else
#define dump(...)
#endif

typedef long long int lli;
typedef pair<int, int> ii;
typedef priority_queue<int, vector<int>, greater<int> > heapq;
int dx[4]={1,0,-1,0};
int dy[4]={0,1,0,-1};
struct aaa{
    aaa(){
        cin.tie(0); ios::sync_with_stdio(0); cout<<fixed<<setprecision(20);
    };
}aaaaaaa;

// #define int long long int
// struct S{
//     bool operator<(const S& x) const {
//         return ;
//     }
// };
signed main() {
    int N; cin >> N;
    map<int, queue<int>* > M;
    rep(i, N) {
        M[i] = new queue<int>();
        rep(j, N - 1) {
            int a; cin >> a;
            a--;
            M[i]->push(a);
        }
    }

    int d = 0;
    int memo[1001];
    bool change, end;
    while (1) {
        change = false;
        ZERO(memo);
        end = true;

        d++;
        for(auto it = M.begin(); it != M.end(); ++it) {
            int i = it->first;
            queue<int>* Q = it->second;
            if (Q->empty()) {
                M.erase(it);
                continue;
            }
            else {
                end = false;
            }
            if (memo[i] == 1) continue;
            int opo = Q->front();
            queue<int> *opoQ = M[Q->front()];
            if (memo[opo] == 1) continue;

            if (opoQ->front() == i) {
                Q->pop();
                opoQ->pop();
                memo[i] = 1;
                memo[opo] = 1;
                change = true;
            }
        }

        if (end) {
            break;
        }
        if (!change) {
            cout << -1 << endl;
            return 0;
        }
    }
    cout << d << endl;
    return 0;
}