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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

-- https://github.com/minoki/my-atcoder-solutions
{-# LANGUAGE BangPatterns #-}
import Data.Char (isSpace)
import Data.List (unfoldr)
import Data.Maybe (fromMaybe)
import Control.Monad
import Control.Monad.ST
import Control.Monad.Trans.Maybe
import Control.Monad.Trans.Class (lift)
import qualified Data.Vector as V
import qualified Data.Vector.Mutable as VM
import qualified Data.Vector.Unboxed as U
import qualified Data.Vector.Unboxed.Mutable as UM
import qualified Data.ByteString.Char8 as BS

-- 有向グラフに閉路があるか判定し、閉路があれば Nothing を返す。
-- 閉路がなければ最長路の長さを返す。
solve :: V.Vector [Int] -> Maybe Int
solve edges = fmap U.maximum $ runST $ runMaybeT $ do
  let !n = V.length edges  -- 頂点の個数
  vec <- UM.replicate n (-2 :: Int) -- -2: new, -1: DFSの最中, 正: チェック済み
  let dfs !x = do
        s <- UM.read vec x
        case s of
          -2 -> do
            -- x を通る閉路があるかチェックする
            UM.write vec x (-1)
            v <- foldM (\ !a y -> max a <$> dfs y) 0 (edges V.! x)
            lift $ do let !v' = v + 1
                      UM.write vec x v'
                      return v'
          -1 -> mzero  -- コールスタックのどこかで dfs x が呼ばれている。閉路
          v -> return v
  mapM_ dfs [0..n-1]
  U.unsafeFreeze vec

main = do
  n <- readLn
  xs <- V.replicateM n $ do
    U.map (subtract 1) . U.unfoldrN (n-1) (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine
  let m = n * (n - 1) `quot` 2  -- グラフの頂点数
  let -- (i,j) (0 <= i < j < n) を 0 以上 m 未満の整数値にコードする
      makePair :: Int -> Int -> Int
      makePair i j | i' < j' = n * i' - (i' + 1) * i' `quot` 2 + j' - i' - 1
                   | otherwise = undefined
        where i' = min i j; j' = max i j
  -- 「試合 (i,j) よりも試合 (i',j') の方を後に行う場合に辺 makePair i j → makePair i' j' が存在する」ようなグラフを作る
  let edges :: V.Vector [Int]
      edges = V.create $ do
        e <- VM.replicate m []
        V.forM_ (V.indexed xs) $ \(i,ys) -> do
          U.forM_ (U.zip ys (U.tail ys)) $ \(a,b) -> do
            -- (i,a) -> (i,b)
            let !b' = makePair i b
            -- VM.modify e (b' :) (makePair i a)
            t <- VM.read e (makePair i a)
            VM.write e (makePair i a) $! b' : t
        return e
  print $ fromMaybe (-1) $ solve edges