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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

def main():
    from sys import setrecursionlimit, stdin, stderr
    from os import environ
    from collections import defaultdict, deque, Counter
    from math import ceil, floor
    from itertools import accumulate, combinations, combinations_with_replacement
    setrecursionlimit(10**6)
    dbg = (lambda *something: stderr.write("\033[92m{}\033[0m".format(str(something)+'\n'))) if 'TERM_PROGRAM' in environ else lambda *x: 0
    input = lambda: stdin.readline().rstrip()
    LMIIS = lambda: list(map(int,input().split()))
    II = lambda: int(input())
    P = 10**9+7
    INF = 10**18+10

    N = II()
    A = []
    for i in range(N):
        A.append(deque(map(lambda x: int(x)-1, input().split())))
    
    dbg('hoge')
    ans = 0
    players = deque(range(N))
    calc = 0
    mathced = False
    next_match = match = defaultdict(lambda : -1)
    first = True
    while True:
        next_players = deque()
        next_match = defaultdict(lambda : -1)
        # dbg('day',ans)
        for i in players:
            # dbg(i,ans,players,A,match)
            calc += 1
            a = A[i]
            if len(a) == 0:
                continue
            j = a[0]
            b = A[j]

            
            
            if match[j] == i:
                # dbg(i,j)
                b.popleft()
                # if b[0] != i:
                #     dbg('fuga')
                a.popleft()
                mathced = True
                match[i] = -1
                match[j] = -1
                if len(a) > 0:
                    next_match[i] = a[0]
                    next_players.append(i)

                if len(b) > 0:
                    next_match[j] = b[0]
                    next_players.append(j)


            else:
                next_match[i] = a[0]

        players = next_players
        match.update(next_match)
        if first:
            dbg('hogehoge')
            first = False
            players = range(N)
            continue
        ans += 1
        if not mathced or len(players) == 0:
            break

        
    print(ans if mathced and len(next_players)==0 else -1)
    dbg(calc)






    

    ans = 0

    

    
   
main()