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 Julia (0.5.0) (judge verdict: Wrong Answer)

const PAIR = Pair{Int,Int}

#################### library ####################


#################### graph ####################

const Graph = Dict{Int,Vector{Int}}
const GraphPAIR = Dict{PAIR,Vector{PAIR}}

# graph: { node: [node] }
function is_cyclic(graph::GraphPAIR)
	for pair in graph
		x0 = pair.first
		v = [x0]	# stack
		s::Set{Pair} = Set{Pair}()
		while !isempty(v)
			x = pop!(v)
			for y in graph[x]
				if !in(y, s)
					push!(s, y)
					push!(v, y)
				end
			end
		end
		
		if in(x0, s)
			return true
		end
	end
	
	return false
end


#################### naive ####################


#################### process ####################

function read_input()
	N = parse(Int, readline())
	table = [ [ parse(Int, s) for s in split(readline()) ] for _ in 1:N ]
	return table
end

function make_graph(table)::GraphPAIR
	function f(v)
		dic::Dict{Int,Int} = Dict()
		k = 0
		for e in v
			dic[e] = k
		end
		return dic
	end
	
	N = length(table)
	dics = [ f(v) for v in table ]
	graph::GraphPAIR = Dict()
	for i in 1:N-1
		for j in i+1:N
			graph[PAIR(i,j)] = []
		end
	end
	for pair in graph
		k = pair.first.first
		l = pair.first.second
		i1 = dics[k][l]
		if i1 < N-1
			j1 = table[k][i1+1]
			push!(graph[Pair(k, l)], minimum([Pair(k, j1), Pair(j1, k)]))
		end
		i2 = dics[l][k]
		if i2 < N-1
			j2 = table[l][i2+1]
			push!(graph[Pair(k, l)], minimum([Pair(l, j2), Pair(j2, l)]))
		end
	end
	return graph
end

function f()
	table = read_input()
	N = length(table)
	memo::Dict{PAIR,Int} = Dict()
	graph::GraphPAIR = make_graph(table)
	if is_cyclic(graph)
		return -1
	end
	
	unvisited = Set(Pair(n, m) for n in 1:N-1 for m in n+1:N)
	for pair in graph
		if length(pair.second) == 0
			memo[pair.first] = 1
			pop!(unvisited, pair.first)
		end
	end
	
	for i in 1:N-1
		for j in i+1:N
			v = Pair(i, j)
			if !in(v, unvisited)
				continue
			end
			stack = [v]
			while !isempty(stack)
				v = pop!(stack)
				unvs = [ v1 for v1 in graph[v] if in(v1, unvisited) ]
				if isempty(unvs)
					dist = maximum([memo[v1]+1 for v1 in graph[v]])
					memo[v] = dist
					pop!(unvisited, v)
				else
					push!(stack, v)
					for v1 in unvs
						push!(stack, v1)
					end
				end
			end
		end
	end
	
	return maximum(pair.second for pair in memo)
end


#################### main ####################

println(f())