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: Time Limit Exceeded)

{-# OPTIONS_GHC -O2 #-}
{-# LANGUAGE BangPatterns #-}
module Main where

import Control.Monad
import Data.Maybe
import qualified Data.Vector.Unboxed as U
import qualified Data.ByteString.Char8 as C

fst3 (x,_,_) = x
snd3 (_,y,_) = y
thd3 (_,_,z) = z

tuplify2 (x:y:_) = (x,y)
tuplify2 _ = undefined

--Input functions with ByteString
readInt = fst . fromJust . C.readInt
readIntTuple = tuplify2 . map readInt . C.words
readIntList = map readInt . C.words

getInt = readInt <$> C.getLine
getIntList = readIntList <$> C.getLine
getIntNList n = map readIntList <$> replicateM (fromIntegral n) C.getLine
getIntMatrix = map readIntList . C.lines <$> C.getContents
getIntTuple = readIntTuple <$> C.getLine
getIntNTuples n = map readIntTuple <$> replicateM (fromIntegral n) C.getLine
getIntTuples = map readIntTuple . C.lines <$> C.getContents

main :: IO ()
main = do
  n <- getInt
  ex <- getIntNList n
  print $ simulate 0 (ini ex)

ini :: [[Int]] -> [(Int, (Int, [Int], State))]
ini = zipWith (\i x -> (i, split' x)) [1..]

data State = Progress | Keep | Done deriving (Show, Eq, Ord)

step :: [(Int, (Int, [Int], State))] -> [(Int, (Int, [Int], State))]
step = zipWith f <$> (U.toList . hs) <*> id
  where
    hs = (U.map <$> f <*> id) . U.fromList . map (fst3.snd)
      where f xs h = if h == 0 then 0 else xs U.! (h-1)
    f h' !(i, (h, !t, s)) | h' == i = (i, split' t)
                          | otherwise = (i, (h, t, if s == Progress then Keep else s))

simulate :: Int -> [(Int, (Int, [Int], State))] -> Int
simulate n ex | any ((Progress==).thd3.snd) ex' = simulate (n+1) ex'
              | all ((Done==).thd3.snd) ex' = n+1
              | otherwise = -1
  where !ex' = step ex
    

split' :: [Int] -> (Int, [Int], State)
split' [] = (0, [], Done)
split' (x:xs) = (x, xs, Progress)