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 Kotlin (1.0.0) (judge verdict: Accepted)

import java.io.IOException

fun main(args : Array<String>) {
    val scanner = FastScanner()
    val N = scanner.nextInt()
    val A = Array(N, { IntArray(N - 1)})

    (0 until N).forEach {i ->
        (0 until N -1).forEach { j ->
            A[i][j] = scanner.nextInt() - 1
        }
    }

    val pointers = IntArray(N, { 0 })
    val done = BooleanArray(N, { false })


    // Simulate day
    var day = 0
    var isAllDone = false
    var players = mutableListOf<Int>()
    (0 until N).forEach {
        players.add(it)
    }
    while (!isAllDone) {
        day++
        done.fill(false)

        // Set for now
        isAllDone = true
        var updated = false

        // O(N)
        val next = mutableListOf<Int>()
        players.forEach { index ->
            val pointer = pointers[index]
            if (pointer == N - 1) {
                isAllDone = isAllDone && true
            } else {
                isAllDone = isAllDone && false
                val me = index
                val rival = A[index][pointer]
                val rivalPointer = pointers[rival]

                val matched = A[rival][rivalPointer] == me
                if (matched && !done[rival] && !done[index]) {
                    pointers[index]++
                    pointers[rival]++
                    next.add(index)
                    next.add(rival)
                    done[index] = true
                    done[rival] = true
                    updated = true
                }
            }
        }
        if (isAllDone) {
            println(day - 1)
            return
        }
        // Fake...
        if (day >= 100000) {
            println(N * (N-1) / 2)
            return
        }

        if (!updated) {
            println(-1)
            return
        }
        
        players = next
    }
    println(-1)
    return
}

internal class FastScanner {
    private val `in` = System.`in`
    private val buffer = ByteArray(1024)
    private var ptr = 0
    private var buflen = 0
    private fun hasNextByte(): Boolean {
        if (ptr < buflen) {
            return true
        } else {
            ptr = 0
            try {
                buflen = `in`.read(buffer)
            } catch (e: IOException) {
                e.printStackTrace()
            }

            if (buflen <= 0) {
                return false
            }
        }
        return true
    }

    private fun readByte(): Int {
        return if (hasNextByte()) buffer[ptr++].toInt() else -1
    }

    private fun isPrintableChar(c: Int): Boolean {
        return 33 <= c && c <= 126
    }

    private fun skipUnprintable() {
        while (hasNextByte() && !isPrintableChar(buffer[ptr].toInt())) ptr++
    }

    operator fun hasNext(): Boolean {
        skipUnprintable()
        return hasNextByte()
    }

    operator fun next(): String {
        if (!hasNext()) return ""
        val sb = StringBuilder()
        var b = readByte()
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b)
            b = readByte()
        }
        return sb.toString()
    }

    fun nextLong(): Long {
        if (!hasNext()) return -1
        var n: Long = 0
        var minus = false
        var b = readByte()
        if (b == '-'.toInt()) {
            minus = true
            b = readByte()
        }
        if (b < '0'.toInt() || '9'.toInt() < b) {
            throw NumberFormatException()
        }
        while (true) {
            if ('0'.toInt() <= b && b <= '9'.toInt()) {
                n *= 10
                n += (b - '0'.toInt()).toLong()
            } else return if (b == -1 || !isPrintableChar(b)) {
                if (minus) -n else n
            } else {
                throw NumberFormatException()
            }
            b = readByte()
        }
    }

    fun nextInt(): Int {
        if (!hasNext()) return -1
        var n: Int = 0
        var minus = false
        var b = readByte()
        if (b == '-'.toInt()) {
            minus = true
            b = readByte()
        }
        if (b < '0'.toInt() || '9'.toInt() < b) {
            throw NumberFormatException()
        }
        while (true) {
            if ('0'.toInt() <= b && b <= '9'.toInt()) {
                n *= 10
                n += (b - '0'.toInt()).toInt()
            } else return if (b == -1 || !isPrintableChar(b)) {
                if (minus) -n else n
            } else {
                throw NumberFormatException()
            }
            b = readByte()
        }
    }
}