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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
	"sort"
	"strconv"
	"strings"
	"time"
)

func main() {
	io := NewIo()
	defer io.Flush()

	n := io.Int()

	aa := make([][]int, n)
	for i := 0; i < n; i++ {
		tmp := make([]int, n-1)
		for j := 0; j < n-1; j++ {
			tmp[j] = io.Int() - 1
		}
		aa[i] = tmp
	}
	ans := calc(aa)
	fmt.Println(ans)
}

func calc(aa [][]int) int {
	n := len(aa)

	t := time.Now()

	indices := make([]int, n)
	visited := make([]bool, n)

	cnt := 0
	days := 0
	for j := 0; j < n*(n-1); j++ {
		//Log("cnt", cnt)

		days++

		tmp := 0
		visited = make([]bool, n)
		for i := 0; i < n; i++ {

			if time.Now().Sub(t).Seconds() > 1.8 {
				return n * (n - 1) / 2
			}

			if visited[i] {
				continue
			}

			if indices[i] >= n-1 {
				continue
			}

			val := aa[i][indices[i]]

			if indices[val] > days-1 {
				continue
			}

			if visited[val] {
				continue
			}

			if aa[val][indices[val]] == i {
				tmp++
				cnt++
				indices[i]++
				indices[val]++
				visited[i] = true
				visited[val] = true

				if cnt == n*(n-1)/2 {
					//Log("day", days)
					return days
				}
			}

			if tmp >= n/2 {
				break
			}
		}
		//Log("indices", indices)

		if tmp == 0 {
			days = -1
			break
		}
	}

	return -1
}

type Io struct {
	reader    *bufio.Reader
	writer    *bufio.Writer
	tokens    []string
	nextToken int
}

func NewIo() *Io {
	return &Io{
		reader: bufio.NewReader(os.Stdin),
		writer: bufio.NewWriter(os.Stdout),
	}
}

func (io *Io) Flush() {
	err := io.writer.Flush()
	if err != nil {
		panic(err)
	}
}

func (io *Io) NextLine() string {
	var buffer []byte
	for {
		line, isPrefix, err := io.reader.ReadLine()
		if err != nil {
			panic(err)
		}
		buffer = append(buffer, line...)
		if !isPrefix {
			break
		}
	}
	return string(buffer)
}

func (io *Io) Next() string {
	for io.nextToken >= len(io.tokens) {
		line := io.NextLine()
		io.tokens = strings.Fields(line)
		io.nextToken = 0
	}
	r := io.tokens[io.nextToken]
	io.nextToken++
	return r
}

func (io *Io) Int() int {
	i, err := strconv.Atoi(io.Next())
	if err != nil {
		panic(err)
	}
	return i
}

func (io *Io) Float() float64 {
	i, err := strconv.ParseFloat(io.Next(), 64)
	if err != nil {
		panic(err)
	}
	return i
}

func (io *Io) PrintLn(a ...interface{}) {
	fmt.Fprintln(io.writer, a...)
}

func (io *Io) Printf(format string, a ...interface{}) {
	fmt.Fprintf(io.writer, format, a...)
}

func (io *Io) PrintIntLn(a []int) {
	b := []interface{}{}
	for _, x := range a {
		b = append(b, x)
	}
	io.PrintLn(b...)
}

func (io *Io) PrintStringLn(a []string) {
	b := []interface{}{}
	for _, x := range a {
		b = append(b, x)
	}
	io.PrintLn(b...)
}

func Log(name string, value interface{}) {
	fmt.Fprintf(os.Stderr, "%s=%+v\n", name, value)
}

func Abs(a int) int {
	if a >= 0 {
		return a
	} else {
		return -a
	}
}

func Pow(p, q int) int {
	return int(math.Pow(float64(p), float64(q)))
}

func Min(nums ...int) int {
	if len(nums) == 0 {
		panic("funciton min() requires at least one argument.")
	}
	res := nums[0]
	for i := 0; i < len(nums); i++ {
		res = int(math.Min(float64(res), float64(nums[i])))
	}
	return res
}

func Max(nums ...int) int {
	if len(nums) == 0 {
		panic("funciton max() requires at least one argument.")
	}
	res := nums[0]
	for i := 0; i < len(nums); i++ {
		res = int(math.Max(float64(res), float64(nums[i])))
	}
	return res
}

func SortAsc(a []int) []int {
	sort.Ints(a)
	return a
}

func SortDesc(a []int) []int {
	sort.Sort(sort.Reverse(sort.IntSlice(a)))
	return a
}

func GCD(a, b int) int {
	if b == 0 {
		return a
	}
	return GCD(b, a%b)
}

func LCM(a, b int) int {
	if a == 0 && b == 0 {
		return 0
	}
	return a * b / GCD(a, b)
}

func CumSum(nums []int) []int {
	sums := []int{0}

	for i := 0; i < len(nums); i++ {
		sums = append(sums, sums[i]+nums[i])
	}
	return sums
}

func BisectLeft(nums []int, left, right int, target int) int {
	if left == right {
		if nums[left] == target {
			return left
		} else if nums[left] < target {
			return left + 1
		} else {
			return left
		}
	}

	mid := (left + right) / 2
	if nums[mid] == target {
		return mid
	}

	if nums[mid] > target {
		return BisectLeft(nums, left, mid, target)
	} else if nums[mid] < target {
		return BisectLeft(nums, mid+1, right, target)
	}
	return 0
}

func Permutations(nums []int) [][]int {
	n := len(nums)
	if n == 0 {
		return [][]int{}
	}
	ans := [][]int{}

	for _, n := range nums {
		rest := remove(nums, n)
		lists := Permutations(rest)
		if len(lists) == 0 {
			lists = [][]int{nil}
		}

		for i := 0; i < len(lists); i++ {
			lists[i] = append(lists[i], n)
			ans = append(ans, lists[i])
		}
	}
	return ans
}

func remove(nums []int, target int) []int {
	result := []int{}
	for i := 0; i < len(nums); i++ {
		if nums[i] != target {
			result = append(result, nums[i])
		}
	}
	return result
}

func PowerSet(nums []int) [][]int {
	size := Pow(2, len(nums))
	result := make([][]int, size)

	idx := 0
	result[idx] = []int{}
	idx++

	for _, n := range nums {
		max := idx
		for i := 0; i < max; i++ {
			result[idx] = copyAndAppend(result[i], n)
			idx++
		}
	}

	return result
}

func copyAndAppend(nums []int, n int) []int {
	dst := make([]int, len(nums)+1)
	copy(dst, nums)
	dst[len(nums)] = n
	return dst
}

func Combination(nums []int, k int) [][]int {
	size := len(nums)
	result := make([][]int, CombinationCount(len(nums), k))
	bi := (1 << uint(k)) - 1
	max := 1 << uint(size)
	idx := 0

	for bi < max {
		flags := bi
		s := []int{}
		for _, n := range nums {
			if flags%2 != 0 {
				s = append(s, n)
			}
			flags /= 2
		}
		result[idx] = s
		idx++
		bi = Combination2NextIndex(bi)
	}
	return result
}

func Combination2NextIndex(n int) int {
	smallest := n & -n
	ripple := n + smallest
	newSmallest := ripple & -ripple
	ones := ((newSmallest / smallest) >> 1) - 1
	return ripple | ones
}

func CombinationCount(n, m int) int {
	return Fact(n) / (Fact(n-m) * Fact(m))
}

func Fact(n int) int {
	if n == 0 {
		return 1
	} else {
		return n * Fact(n-1)
	}
}

func Divisors(n int) []int {
	divisors := map[int]bool{}
	for i := 1; i < int(math.Sqrt(float64(n)))+1; i++ {
		if n%i == 0 {
			divisors[i] = true
			//divisors = append(divisors, i)
			if i != n {
				divisors[n/i] = true
				//divisors = append(divisors, n/i)
			}
		}

	}
	ans := []int{}
	for k := range divisors {
		ans = append(ans, k)
	}
	return ans
}