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 OCaml (4.02.3) (judge verdict: Time Limit Exceeded)

open Printf
open Scanf

let read_intlist: unit -> int list = fun () ->
  let sl = Str.split (Str.regexp " ") @@ read_line () in
  List.map (fun s -> sscanf s "%d" (fun x -> x)) sl

let n = sscanf (read_line ()) "%d" (fun x -> x)
let a: int array array = Array.make (n+1) [|0|]
let () = for y = 1 to n do
           a.(y) <- 0 :: (read_intlist ()) @ [0] |> Array.of_list
         done

(*  *)
let ans = ref 0
let inds = Array.make (n+1) 1

let () =
  let bflag = ref true in
  while !bflag do
    let dp = Array.make (n+1) false in
    let flag = ref true in

    for i = 1 to n do
      let x = inds.(i) in
      if not dp.(i) && x < n then begin
        let target = a.(i).(x) in
        if not dp.(target) && a.(target).(inds.(target)) = i then begin
            dp.(i) <- true;
            dp.(target) <- true;

            inds.(i) <- inds.(i) + 1;
            inds.(target) <- inds.(target) + 1;

            if !flag then
              flag := false
          end
        end;
    done;

    if !flag then
      let hoge = List.tl (Array.to_list inds)
                 |> List.for_all (fun e -> e = n) in
      if hoge then
        bflag := false
      else begin
          ans := -1;
          bflag := false
        end
    else
      incr ans
  done

let () = print_endline @@ string_of_int !ans