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.chomp.to_i
a=Array.new
for i in 0..n-1
  a[i]=gets.chomp.split(" ").map{|s| s.to_i}
end
le=[]
for i in 0..n-1
  le[i]=[a[i][0],0]
end
#le[番目の選手][番目の勝負]
#le[i番目の選手][0番目の勝負]
ans=1
while true
  ud=[] #更新のための配列
  for i in 0..n-1
    t=le[i][0]-1 #対戦相手の指定
    if i+1==le[t][0] #一致
      ud.push(i)
    end
  end
  if ud[0]==nil
    puts -1
    break
  else
    ud.each do |i|
      q=le[i][1] #何番目の勝負か
      le[i]=[a[i][q+1],q+1] if le[i][1]!=n-2
    end
  end

  ans+=1
  f=true
  for i in 0..n-1
    f=false if le[i][1]!=n-2
  end
  if f
    puts ans
    break
  end
end