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 (2.4.0) (judge verdict: Accepted)

import sys
sys.setrecursionlimit(2147483647)
INF=float("inf")
MOD=10**9+7
input=lambda:sys.stdin.readline().rstrip()
def resolve():
    n=int(input())
    M=[None]*n
    for i in range(n):
        M[i]=list(map(lambda x:int(x)-1,input().split()))[::-1]

    # i が誰かしらと対戦できるか
    def check(i):
        if(not M[i]): # 既に試合を終えている
            return False
        j=M[i][-1]
        if(not M[j]): # これは起こり得ない
            return False
        return i==M[j][-1]

    # 初日に対戦できる人をピックアップ
    # 重複が起こるが、後で unique を取る
    Q=[]
    for i in range(n):
        if(check(i)):
            j=M[i][-1]
            if(i>j): i,j=j,i # i<j
            Q.append((i,j))

    # 処理を行なっていく
    day=0
    nQ=[] # 次の試合相手
    while(Q):
        # Q には重複があるので unique
        Q=list(set(Q))
        # 先に全ての試合を終わらせる必要がある
        for i,j in Q:
            M[i].pop(); M[j].pop()
        # 試合を終えた人は次の試合を行える可能性がある
        for i,j in Q:
            if(check(i)):
                k=M[i][-1]
                nQ.append((min(i,k),max(i,k)))
            if(check(j)):
                k=M[j][-1]
                nQ.append((min(j,k),max(j,k)))
        Q,nQ=nQ,[]
        day+=1

    print(day if(all(M[i]==[] for i in range(n))) else "-1")
resolve()