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: Time Limit Exceeded)

import java.io.*
import java.lang.*
import java.math.*
import java.util.*

// Constant

val sc = FastScanner()
val pw = PrintWriter(System.out)
const val MOD = 1000000007L
const val INF = 9223372036854775807L

// Main

fun main(args: Array<String>) {
    solve()
    pw.flush()
}

// Global

fun solve() {
    val n = nextLong().toInt()
    val a = Array(n) { ArrayDeque<Int>() }
    for (i in 0 until n) {
        repeat(n - 1) {
            a[i].add(nextLong().toInt() - 1)
        }
    }

    var ans = 0
    val flag = BitSet(n)
    var emptyCount = 0
    while (emptyCount < n) {
        emptyCount = 0
        var battle = false
        flag.clear()
        for (i in 0 until n) {
            if(flag[i]) continue
            when {
                a[i].isEmpty() -> {
                    emptyCount++
                    flag[i] = true
                }
                else -> {
                    val enemy = a[i].peek()
                    val res1 = !flag[enemy]
                    val res2 = a[enemy].isNotEmpty()
                    val res3 = if(res2) a[enemy].peek() == i else false
                    if(res1 && res2 && res3) {
                        flag[i] = true
                        flag[enemy] = true
                        battle = true
                        a[i].poll()
                        a[enemy].poll()
                    }
                }
            }

        }
        if(emptyCount == n) break
        if(!battle) {
            println(-1)
            return
        }
        ans++
    }

    println(ans)

}





// Rule

operator fun String.get(index: Long): Char {
    if (index !in 0L..Int.MAX_VALUE) throw IllegalArgumentException()
    return this[index.toInt()]
}
operator fun CharArray.get(index: Long): Char {
    if (index !in 0L..Int.MAX_VALUE) throw IllegalArgumentException()
    return this[index.toInt()]
}
operator fun CharArray.set(index: Long, value: Char) {
    if (index !in 0L..Int.MAX_VALUE) throw IllegalArgumentException()
    this[index.toInt()] = value
}
operator fun IntArray.get(index: Long): Int {
    if (index !in 0L..Int.MAX_VALUE) throw IllegalArgumentException()
    return this[index.toInt()]
}
operator fun IntArray.set(index: Long, value: Int) {
    if (index !in 0L..Int.MAX_VALUE) throw IllegalArgumentException()
    this[index.toInt()] = value
}
operator fun LongArray.get(index: Long): Long {
    if (index !in 0L..Int.MAX_VALUE) throw IllegalArgumentException()
    return this[index.toInt()]
}
operator fun LongArray.set(index: Long, value: Long) {
    if (index !in 0L..Int.MAX_VALUE) throw IllegalArgumentException()
    this[index.toInt()] = value
}
operator fun DoubleArray.get(index: Long): Double {
    if (index !in 0L..Int.MAX_VALUE) throw IllegalArgumentException()
    return this[index.toInt()]
}
operator fun DoubleArray.set(index: Long, value: Double) {
    if (index !in 0L..Int.MAX_VALUE) throw IllegalArgumentException()
    this[index.toInt()] = value
}
operator fun <T> Array<T>.get(index: Long): T {
    if (index !in 0L..Int.MAX_VALUE) throw IllegalArgumentException()
    return this[index.toInt()]
}
operator fun <T> Array<T>.set(index: Long, value: T) {
    if (index !in 0L..Int.MAX_VALUE) throw IllegalArgumentException()
    this[index.toInt()] = value
}
operator fun <T> MutableList<T>.get(index: Long): T {
    if (index !in 0L..Int.MAX_VALUE) throw IllegalArgumentException()
    return this[index.toInt()]
}
operator fun <T> MutableList<T>.set(index: Long, value: T) {
    if (index !in 0L..Int.MAX_VALUE) throw IllegalArgumentException()
    this[index.toInt()] = value
}

val LongArray.siz: Long
    get() = size.toLong()
val <T> Array<T>.siz: Long
    get() = size.toLong()
val <T> MutableList<T>.siz: Long
    get() = size.toLong()
val <T> MutableSet<T>.siz: Long
    get() = size.toLong()
val String.len: Long
    get() = length.toLong()

// Output

fun println(v: String) {
    pw.println(v)
}
fun print(v: String) {
    pw.print(v)
}

// Input

fun next() = sc.next()
fun nextLong() = sc.nextLong()
fun nextLongs() = readLine()!!.split(" ").map { it.toLong() }
fun nextDouble() = next().toDouble()
fun nextAry(n: Long): Array<String> {
    val ary = ary(n)
    for (i in 0 until n) ary[i] = next()
    return ary
}
fun nextLongAry(n: Long): LongArray {
    val ary = longAry(n)
    for (i in 0 until n) ary[i] = nextLong()
    return ary
}
fun nextDoubleAry(n: Long): DoubleArray {
    val ary = doubleAry(n)
    for (i in 0 until n) ary[i] = nextDouble()
    return ary
}

// Statement

fun ary(n: Long, init: String = "") = Array(n.toInt()) { init }
fun longAry(n: Long, init: Long = 0L) = LongArray(n.toInt()) { init }
fun doubleAry(n: Long, init: Double = 0.0) = DoubleArray(n.toInt()) { init }
fun boolAry(n: Long, init: Boolean = false) = Array(n.toInt()) { init }
fun nodeAry(n: Long) = Array(n.toInt()) { Node(it.toLong()) }
fun ary2(n: Long, m: Long, init: String = "") = Array(n.toInt()) { ary(m, init) }
fun longAry2(n: Long, m: Long, init: Long = 0) = Array(n.toInt()) { longAry(m, init) }
fun doubleAry2(n: Long, m: Long, init: Double = 0.0) = Array(n.toInt()) { doubleAry(m, init) }
fun boolAry2(n: Long, m: Long, init: Boolean = false) = Array(n.toInt()) { boolAry(m, init) }
fun ary3(n: Long, m: Long, k: Long, init: String = "") = Array(n.toInt()) { ary2(m, k, init) }
fun longAry3(n: Long, m: Long, k: Long, init: Long = 0L) = Array(n.toInt()) { longAry2(m, k, init) }
fun doubleAry3(n: Long, m: Long, k: Long, init: Double = 0.0) = Array(n.toInt()) { doubleAry2(m, k, init) }
fun boolAry3(n: Long, m: Long, k: Long, init: Boolean = false) = Array(n.toInt()) { boolAry2(m, k, init) }
fun list() = mutableListOf<String>()
fun longList() = mutableListOf<Long>()
fun doubleList() = mutableListOf<Double>()
fun strSet() = mutableSetOf<String>()
fun longSet() = mutableSetOf<Long>()
fun doubleSet() = mutableSetOf<Double>()
fun <E, V> map() = mutableMapOf<E, V>()

// Monoid

val addFunc = {a: Long, b: Long -> a + b}
val mulFunc = {a: Long, b: Long -> a * b}
val maxFunc = {a: Long, b: Long -> max(a, b)}
val minFunc = {a: Long, b: Long -> min(a, b)}
val gcdFunc = {a: Long, b: Long -> gcd(a, b)}
val lcmFunc = {a: Long, b: Long -> lcm(a, b)}
val xorFunc = {a: Long, b: Long -> a xor b}
fun calc(a: Long, b: Long, op: (Long, Long) -> Long) = op(a, b)

// Extension

fun LongArray.lowerBound(n: Long): Long {
    var ok = this.size.toLong()
    var ng = -1L
    while (abs(ok - ng) > 1) {
        val mid = (ok + ng) / 2
        if (this[mid] >= n) ok = mid
        else ng = mid
    }
    return ok
}
fun DoubleArray.lowerBound(n: Double): Long {
    var ok = this.size.toLong()
    var ng = -1L
    while (abs(ok - ng) > 1) {
        val mid = (ok + ng) / 2
        if (this[mid] >= n) ok = mid
        else ng = mid
    }
    return ok
}
fun MutableList<Long>.longLowerBound(n: Long): Long {
    var ok = this.size.toLong()
    var ng = -1L
    while (abs(ok - ng) > 1) {
        val mid = (ok + ng) / 2
        if (this[mid] >= n) ok = mid
        else ng = mid
    }
    return ok
}
fun MutableList<Double>.doubleLowerBound(n: Double): Long {
    var ok = this.size.toLong()
    var ng = -1L
    while (abs(ok - ng) > 1) {
        val mid = (ok + ng) / 2
        if (this[mid] >= n) ok = mid
        else ng = mid
    }
    return ok
}
fun LongArray.cumsum(op: (Long, Long) -> Long): LongArray {
    val s = longAry(this.size + 1L)
    s[1] = this[0]
    for (i in 1 until this.size) s[i + 1] = calc(s[i], this[i], op)
    return s
}
fun MutableMap<String, Int>.counting(n: Long) {
    repeat(n.toInt()) {
        val a = next()
        if (this.containsKey(a)) this[a] = this[a]!! + 1
        else this[a] = 1
    }
}
fun MutableMap<Long, Int>.longCounting(n: Long) {
    repeat(n.toInt()) {
        val a = nextLong()
        if (this.containsKey(a)) this[a] = this[a]!! + 1
        else this[a] = 1
    }
}

// Mathematics

fun abs(n: Long): Long = Math.abs(n)
fun abs(n: Double): Double = Math.abs(n)
fun max(vararg values: Long) = if (values.isEmpty()) -INF else values.max()!!
fun min(vararg values: Long) = if (values.isEmpty()) INF else values.min()!!
tailrec fun gcd(a: Long, b: Long): Long = if (b == 0L) a else if (a % b == 0L) b else gcd(b, (a % b))
fun lcm(a: Long, b: Long): Long = a / gcd(a, b) * b
fun erathos(n: Long): LongArray {
    val res = LongArray(n.toInt() + 1) { it.toLong() }
    for (i in 2..n) {
        if(i * i > n) break
        for (j in i * i..n step i) {
            if(res[j] == j) res[j] = i
        }
    }
    res[0] = -1L
    res[1] = -1L
    return res
}
fun modAdd(a: Long, b: Long) = if(a + b >= MOD) a + b - MOD else a + b
fun modpow(a: Long, n: Long, p: Long = MOD): Long {
    var res = 1L
    var ar = a
    var nr = n
    while (nr > 0) {
        if ((nr and 1) == 1L) res = res * ar % p
        ar = ar * ar % p
        nr = nr shr 1
    }
    return res
}
fun modinv(a: Long, p: Long = MOD): Long = modpow(a, p - 2, p)
fun ncr(n: Long, r: Long): Long {
    var a = 1L
    var b = 1L
    for (i in 1..r) {
        a = a * (n + 1 - i) % MOD
        b = b * i % MOD
    }
    return modinv(b, MOD) * a % MOD
}

class Combination(private val max: Long) {
    private val fac = longAry(max)
    private val finv = longAry(max)
    private val inv = longAry(max)
    private val p = MOD
    fun init() {
        fac[0] = 1
        fac[1] = 1
        finv[0] = 1
        finv[1] = 1
        inv[1] = 1
        for (i in 2 until max) {
            fac[i] = fac[i - 1] * i % p
            inv[i] = p - inv[p % i] * (p / i) % p;
            finv[i] = finv[i - 1] * inv[i] % p
        }
    }

    fun com(n: Long, r: Long): Long = if (n < r || (n < 0 || r < 0)) 0L else fac[n] * (finv[r] * finv[n - r] % p) % p
}

class Permutation(private val n: Long, private var searched: Long = 0L, private var nextIndex: Long = 0L) {
    private val size = fact(n)
    private val permList = longAry2(size, n)

    private tailrec fun fact(n: Long, ans: Long = 1L): Long {
        return if (n == 0L) ans
        else fact(n - 1, ans * n)
    }

    fun init() {
        create(0, longAry(n), boolAry(n))
    }

    private fun create(num: Long, list: LongArray, flag: Array<Boolean>) {
        if (num == n) {
            permList[searched] = list.copyOf()
            searched++
        }
        for (i in 0 until n) {
            if (flag[i]) continue
            list[num] = i
            flag[i] = true
            create(num + 1, list, flag)
            flag[i] = false
        }
    }

    fun hasNext(): Boolean {
        return if (nextIndex < size) {
            true
        } else {
            nextIndex = 0
            false
        }
    }

    fun nextPerm(): LongArray = permList[nextIndex++]
}

// String

fun zAlgo(s: String): LongArray {
    val n = s.len
    val res = longAry(n)
    var i = 1L
    var j = 0L
    while(i < n) {
        while (i + j < n && s[j] == s[i + j]) j++
        res[i] = j
        if(j == 0L) {
            i++
            continue
        }
        var k = 1L
        while (i + k < n && k + res[k] < j) {
            res[i + k] = res[k]
            k++
        }
        i += k
        j -= k
    }

    return res
}

// Graph

data class Node(val id: Long, var past: Long = -1, val edges: MutableList<Edge> = mutableListOf())
data class Edge(val from: Long, val to: Long, val cost: Long = 1L)

fun dfs(nodes: Array<Node>, now: Long, seen: Array<Boolean>) {
    seen[now] = true
    for (edge in nodes[now].edges) {
        if (seen[edge.to]) continue
        dfs(nodes, edge.to, seen)
    }
}

fun bfs(nodes: Array<Node>, start: Long): LongArray {
    val queue = ArrayDeque<Long>()
    queue.add(start)
    val dist = longAry(nodes.size.toLong(), -1L)
    dist[start] = 0L
    while (queue.isNotEmpty()) {
        val now = queue.poll()
        for (edge in nodes[now].edges) {
            if (dist[edge.to] != -1L) continue
            dist[edge.to] = dist[now] + 1
            queue.add(edge.to)
        }
    }
    return dist
}

fun dijkstra(nodes: Array<Node>, start: Long): LongArray {
    val queue = PriorityQueue(16) { e1: Edge, e2: Edge ->
        return@PriorityQueue when {
            e1.cost < e2.cost -> -1
            e2.cost > e1.cost -> 1
            else -> 0
        }
    }
    queue.add(Edge(start, start, 0L))
    val dist = longAry(nodes.size.toLong(), INF / 2)
    dist[start] = 0
    while (queue.isNotEmpty()) {
        val now = queue.poll()
        if (dist[now.to] < now.cost) continue;
        for (edge in nodes[now.to].edges) {
            if (dist[edge.to] <= dist[edge.from] + edge.cost) continue
            dist[edge.to] = dist[edge.from] + edge.cost
            queue.add(Edge(edge.from, edge.to, dist[edge.to]))
            nodes[edge.to].past = edge.from
        }
    }
    return dist
}

class GridGraph(
    private val h: Long,
    private val w: Long,
    val nodes: Array<Node> = Array((h * w).toInt()) { Node(it.toLong()) },
    private val edges: IntArray = IntArray((h * w).toInt()) { 0 }
) {
    private val up = 1
    private val right = 2
    private val down = 4
    private val left = 8
    private val queue: ArrayDeque<Long> = ArrayDeque()
    private val startPos = longList()

    private fun pos(y: Long, x: Long) = y * w + x
    fun canUp(v: Long) = (edges[v] and 1) == 1
    fun canRight(v: Long) = ((edges[v] shr 1) and 1) == 1
    fun canDown(v: Long) = ((edges[v] shr 2) and 1) == 1
    fun canLeft(v: Long) = ((edges[v] shr 3) and 1) == 1

    fun init(s: Array<String>, check: Char = '.', road: Char = '.', start: Char = 'S') {
        for (i in 0 until h) {
            for (j in 0 until w) {
                if(s[i][j] != check && s[i][j] != start) continue
                if(i > 0 && s[i - 1][j] == road) edges[pos(i, j)] += up
                if(i < h - 1 && s[i + 1][j] == road) edges[pos(i, j)] += down
                if(j > 0 && s[i][j - 1] == road) edges[pos(i, j)] += left
                if(j < w - 1 && s[i][j + 1] == road) edges[pos(i, j)] += right
                if(s[i][j] == start) {
                    queue.add(pos(i, j))
                    startPos.add(pos(i, j))
                }
            }
        }
    }
    fun addStart(y: Long, x: Long) {
        startPos.add(pos(y, x))
        queue.add(pos(y, x))
    }

    fun bfs(): LongArray {
        val dist = longAry(h * w, -1L)
        for (i in startPos) {
            dist[i] = 0L
        }
        while (queue.isNotEmpty()) {
            val v = queue.poll()
            if(canUp(v) && dist[v - w] == -1L) {
                queue.add(v - w)
                dist[v - w] = dist[v] + 1L
            }
            if(canDown(v) && dist[v + w] == -1L) {
                queue.add(v + w)
                dist[v + w] = dist[v] + 1L
            }
            if(canLeft(v) && dist[v - 1] == -1L) {
                queue.add(v - 1)
                dist[v - 1] = dist[v] + 1L
            }
            if(canRight(v) && dist[v + 1] == -1L) {
                queue.add(v + 1)
                dist[v + 1] = dist[v] + 1L
            }
        }
        return dist
    }

}

// Data Structure

class UnionFind(size: Long) {
    private val par = LongArray(size.toInt()) { it.toLong() }
    private val size = longAry(size, 1L)
    private val diffWeight = longAry(size, 0L)
    fun root(x: Long): Long {
        return if (par[x] == x) {
            x
        } else {
            val r = root(par[x])
            diffWeight[x] += diffWeight[par[x]]
            par[x] = r
            par[x]
        }
    }
    fun weight(x: Long): Long {
        root(x)
        return diffWeight[x]
    }
    fun diff(x: Long, y: Long) = abs(weight(y) - weight(x))

    fun same(x: Long, y: Long): Boolean = root(x) == root(y)
    fun unite(x: Long, y: Long, d: Long) {
        var w = d
        w += weight(x)
        w -= weight(y)
        var a = root(x)
        var b = root(y)
        if (a == b) return
        if (size[a] < size[b]) {
            var tmp = a
            a = b
            b = tmp
            w = -w
        }
        size[a] += size[b]
        par[b] = a
        diffWeight[b] = w
    }

    fun size(x: Long): Long = size[root(x)]
}

class SegmentTree(
    private val a: LongArray,
    private val op: (Long, Long) -> Long,
    private val def: Long = 0,
    private val size: Int = a.size,
    private val n: Int = Integer.highestOneBit(size) shl 1
) {
    private val nodes = longAry(2L * n - 1, def)

    fun init() {
        for (i in 0 until size) nodes[i + n - 1] = a[i]
        for (i in n - 2 downTo 0) nodes[i] = calc(nodes[2 * i + 1], nodes[2 * i + 2], op)
    }

    fun update(x: Long, value: Long) {
        var index = x + n - 1
        nodes[index] = value
        while (index > 0) {
            index = (index - 1) / 2
            nodes[index] = calc(nodes[2 * index + 1], nodes[2 * index + 2], op)
        }
    }

    fun get(a: Long, b: Long) = getSub(a, b, 0L, 0L, n.toLong())
    private fun getSub(a: Long, b: Long, k: Long, l: Long, r: Long): Long {
        return when {
            r <= a || b <= l -> def
            a <= l && r <= b -> nodes[k]
            else -> {
                val vl = getSub(a, b, k * 2 + 1, l, (l + r) / 2)
                val vr = getSub(a, b, k * 2 + 2, (l + r) / 2, r)
                calc(vl, vr, op)
            }
        }
    }

    fun joinToString(separator: String) = nodes.drop(n - 1).take(size).joinToString(separator)
}

// Scanner

class FastScanner {
    private val sin: InputStream = System.`in`
    private val buffer: ByteArray = ByteArray(1024) { 0 }
    private var ptr = 0
    private var buflen = 0

    private fun hasNextByte(): Boolean {
        return when {
            ptr < buflen -> true
            else -> {
                ptr = 0
                buflen = sin.read(buffer)
                buflen > 0
            }
        }
    }

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

    private fun isPrintableChar(c: Int) = c in 33..126

    fun hasNext(): Boolean {
        while (hasNextByte() && !isPrintableChar(buffer[ptr].toInt())) ptr++
        return hasNextByte()
    }

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

    fun nextLong(): Long {
        if (!hasNext()) throw NoSuchElementException()
        var n = 0L
        var minus = false
        var b = readByte()
        if (b.toChar() == '-') {
            minus = true
            b = readByte()
        }
        if (b.toChar() !in '0'..'9') throw NumberFormatException()
        while (true) {
            when {
                b.toChar() in '0'..'9' -> {
                    n *= 10
                    n += b.toChar() - '0'
                }
                b == -1 || !isPrintableChar(b) -> return if (minus) -n else n
                else -> throw NumberFormatException()
            }
            b = readByte()
        }
    }

//    "The world doesn't need you."
//
//    fun nextInt(): Int {
//        val nl = nextLong()
//        if (nl !in Int.MIN_VALUE..Int.MAX_VALUE) throw NumberFormatException()
//        return nl.toInt()
//    }
}