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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

n = gets.to_i

class Player
  attr_accessor :id, :battle_orders, :possible_game

  def initialize(id, battle_orders, possible_game)
    @id = id
    @battle_orders = battle_orders
    @possible_game = possible_game
  end

  def next_opponent_id
    battle_orders.first - 1
  end

  def battle
    battle_orders.shift
    self.possible_game = false
  end

  def finish?
    battle_orders.empty?
  end

  def reset
    self.possible_game = true if possible_game == false
  end
end

players = []
n.times do |i|
  players << Player.new(i, gets.split.map(&:to_i), true)
end

day = 0
until players.select!{|p| !p.battle_orders.empty?} == []
  day += 1
  flg = true
  players.each(&:reset)
  players.each do |player|
    next if player.finish?
    opponent_player = players.select{|p| p.id == player.next_opponent_id}.first
    next if opponent_player.next_opponent_id != player.id || opponent_player.finish?
    if player.possible_game && opponent_player.possible_game
      flg = false
      player.battle
      opponent_player.battle
    end
  end
  if flg
    p -1
    exit
  end
end
p day