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: Time Limit Exceeded)

import sys
import math
import heapq
sys.setrecursionlimit(10**7)
INTMAX = 9223372036854775807
INTMIN = -9223372036854775808
DVSR = 1000000007
def POW(x, y): return pow(x, y, DVSR)
def INV(x, m=DVSR): return pow(x, m - 2, m)
def DIV(x, y, m=DVSR): return (x * INV(y, m)) % m
def LI(): return [int(x) for x in input().split()]
def LF(): return [float(x) for x in input().split()]
def LS(): return input().split()
def II(): return int(input())
def FLIST(n):
    res = [1]
    for i in range(1, n+1): res.append(res[i-1]*i%DVSR)
    return res
def gcd(x, y):
    if x < y: x, y = y, x
    div = x % y
    while div != 0:
        x, y = y, div
        div = x % y
    return y

N=II()
MATCHES = [[(0,0) for _ in range(N-1)] for _ in range(N)]

for i in range(N):
    lis = LI()
    for j in range(N-1):
        if i+1 < lis[j]:
            MATCHES[i][j] = (i+1, lis[j])
        else:
            MATCHES[i][j] = (lis[j], i+1)

CONT = True
IDXS=[0]*N
DONE=[False]*N
days = 0
ST=set()
while CONT:
    cont = False
    ST.clear()
    for i in range(N): DONE[i] = False
    for i in range(N):
        if IDXS[i] < N-1:
            if MATCHES[i][IDXS[i]] in ST:
                if not DONE[MATCHES[i][IDXS[i]][0]-1] and not DONE[MATCHES[i][IDXS[i]][1]-1]:
                    ST.remove(MATCHES[i][IDXS[i]])
                    DONE[MATCHES[i][IDXS[i]][0]-1] = True
                    DONE[MATCHES[i][IDXS[i]][1]-1] = True
                    # print("{}: {}".format(days, MATCHES[i][IDXS[i]]))
                    if IDXS[i] < N-1:
                        IDXS[MATCHES[i][IDXS[i]][0]-1] += 1
                        IDXS[MATCHES[i][IDXS[i]][1]-1] += 1
                        cont = True
            else:
                # print("add:{}".format(MATCHES[i][IDXS[i]]))
                ST.add(MATCHES[i][IDXS[i]])
    # print(ST)
    CONT = cont
    days += cont


# print(IDXS)
if sum(IDXS) == N*(N-1):
    print(days)
else:
    print(-1)