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: Wrong Answer)

debug = false

N = gets.to_i
orders = []
N.times do
  orders << gets.split.map { |char| char.to_i - 1 }
end

continue_flag = true
day = 0

while continue_flag
  day += 1
  vacant_players = (0...N).to_a
  match = 0
  p orders if debug

  vacant_players.each do |player|
    puts "player: #{player}" if debug
    if vacant_players.include?(player) && !orders[player].nil?
      opposite = orders[player][0]
      if vacant_players.include?(opposite) && orders[opposite][0] == player

        # 試合を組む
        vacant_players.delete(player)
        vacant_players.delete(opposite)

        # 消化
        orders[player] = orders[player][1..-1].empty? ? nil : orders[player][1..-1]
        orders[opposite] = orders[opposite][1..-1].empty? ? nil : orders[opposite][1..-1]

        # 試合が組めました
        match += 1
      end
    end
  end
  puts "day: #{day}, match: #{match}, vacant: #{vacant_players}" if debug

  puts "" if debug

  if orders.compact.empty?
    # 全パターン消化できた"アガリ"パターン
    continue_flag = false
    puts day
  elsif match == 0
    # デッドロックがかかった"ハズレ"パターン
    continue_flag = false
    puts "-1"
  end
end