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 Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program kadai
    implicit none
integer  ::  n
integer,allocatable  ::  a(:,:)
integer,allocatable  ::  now(:)
integer,allocatable  ::  rest(:)
integer  ::  i,j,move,day,num,for

read(*,*) n
allocate(a(n,n-1))
allocate(now(n))
allocate(rest(n))

do i=1,n
    read(*,*) a(i,:)
end do

now=1
rest=0
move=0
num=0
day=1

do j=1,n*n
    do i=1,n
    if(now(i)<n) then
        for=a(i,now(i))

        if (now(for)>n-1) then
            write(*,*) -1
            stop
        end if

        if (a(for,now(for))==i .and. rest(for)==0 .and. rest(i)==0) then
            !write(*,*) i,"vs",for
            now(i)=now(i)+1
            now(for)=now(for)+1
            if (now(i)>n .or. now(for)>n) then
                write(*,*) -1
                !write(*,*) now,num
                stop
            end if
            move=1
            num=num+1
            rest(i)=1
            rest(for)=1
        end if
        if (num==n*(n-1)/2) then
            write(*,*) day
            stop
        end if
    end if
    end do
    if (move==0) then
        write(*,*) -1
        stop
    end if
    day=day+1
    rest=0
end do

write(*,*) -1


stop
contains

end program kadai