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)

def is_loop? n_pos, pos ,tree
  tree[n_pos].include? pos
end

def find_and_remove_zero_indegree_vertexes tree
 keys = tree.keys
 vertexes = tree.values.flatten.uniq
 (keys - vertexes).each do |v|
   tree.delete v
 end
 tree
end

N=gets.chomp.to_i

ARY=[]
# 試合形式で配列に入れる。
N.times do |i|
  ARY << gets.chomp.split.map(&:to_i).zip([i+1]*(N-1))
end

all_games = (1..N).to_a.combination(2).to_a
indexed_games = all_games.each_with_object({}).with_index do |(game, hash),idx|
  hash[game] = idx
end
tree = (0..((N-1)*N/2 - 1)).each_with_object({}) do |i,hash|
  hash[i] = []
end


begin
  ARY.each do |attr|
    pos = indexed_games[attr.shift.sort]
    attr.each do |game|
        n_pos = indexed_games[game.sort]
        tree[pos] << n_pos
        pos = n_pos
        raise if is_loop? n_pos, pos, tree
    end
  end
  cnt = 0
  until tree.keys.empty? do
    find_and_remove_zero_indegree_vertexes tree
    cnt += 1
  end
  puts cnt
rescue
  puts -1
end