module Graphical
	require 'set'

	def get_path_by_bfs(s, t)
		prev_node = {}
		reached = Set[s]
		queue = [s]
		while !queue.empty? 
			u = queue.shift
			each_out_connection_of(u){|v, _|
				next if reached.include?(v)	
				reached << v
				queue << v
				prev_node[v] = u

				if v == t
					path = [v]
					while v = prev_node[v]
						path.unshift v
					end
					return path
				end
			}
		end	
		return nil
	end

	def get_path_by_dfs(s, t, reached = Set.new)
		reached << s
		return [s] if s == t
		each_out_connection_of(s){|v|
			next if reached.include?(v)
			path = get_path_by_dfs(v, t, reached) 
			return [s] + path if path
		}
		nil
	end

	def reachable_from(s, max_depth = nil)
		reached = Set[s]
		queue = [s]
		depth = 0
		loop {
			break if max_depth && depth >= max_depth
			next_queue = []
			until queue.empty?
				u = queue.shift
				each_out_connection_of(u){|v, _|
					next if reached.include?(v)
					reached << v
					next_queue << v
				}
			end
			break if next_queue.empty?
			queue = next_queue
			depth += 1
		}
		return reached
	end

	def bfs(start)
		raise "start must be Enumerable" if !start.kind_of?(Enumerable)
		reached = Set[*start.to_a]
		queue = []
		start.each{|s| queue << s}
		dist = {}
		loop.with_index {|_, depth|
			next_queue = []
			until queue.empty?
				u = queue.shift
				return depth if block_given? && yield(u, depth)
				dist[u] = depth
				each_out_connection_of(u){|v, _|
					next if reached.include?(v)
					reached << v
					next_queue << v
				}
			end
			break if next_queue.empty?
			queue = next_queue
		}
		block_given? ? nil : dist
	end

	def dijkstra(start)
		raise "start must be Enumerable" if !start.kind_of?(Enumerable)
		h = Heap.new
		reached = Set[*start.to_a]
		start.each{|s| h.add(s, 0)}

		dist = {}
		until h.empty?
			u, key = h.del_min
			return key if block_given? && yield(u, key)
			dist[u] = key
			each_out_connection_of(u){|v, l|
				d = dist[u] + l
				if reached.include?(v)
					h.update_key(v, d)
				else
					h.add(v, d)
					reached << v
				end
			}
		end
		block_given? ? nil : dist
	end

	def bidir_dijkstra(s, t)
		f_dist = {}
		b_dist = {}

		f_heap = Heap.new
		b_heap = Heap.new

		f_heap.add(s, 0)
		b_heap.add(t, 0)

		f_reached = Set[s]
		b_reached = Set[t]

		f_current_dist = b_current_dist = 0
		best = Float::INFINITY

		loop {
			if !f_heap.empty?
				u, key = f_heap.del_min
				f_dist[u] = key
				f_current_dist = key
				each_out_connection_of(u){|v, l|
					d = f_dist[u] + l
					if b_dist[v]
						path_len = d + b_dist[v]
						best = path_len if path_len < best
					end
					if f_reached.include?(v)
						f_heap.update_key(v, d)
					else
						f_heap.add(v, d)
						f_reached << v
					end
				}
			end

			if !b_heap.empty?
				u, key = b_heap.del_min
				b_dist[u] = key
				b_current_dist = key
				each_in_connection_of(u){|v, l|
					d = b_dist[u] + l
					if f_dist[v]
						path_len = d + f_dist[v]
						best = path_len if path_len < best
					end
					if b_reached.include?(v)
						b_heap.update_key(v, d)
					else
						b_heap.add(v, d)
						b_reached << v
					end
				}
			end

			return best if f_current_dist + b_current_dist >= best
			return nil if f_heap.empty? && b_heap.empty?
		}
	end

	def a_star(start)
		raise "a_star need termination condition" unless block_given?
		h = Heap.new
		reached = Set[start]
		h.add(start, [a_star_heuristic(start), 0])

		dist = {}
		until h.empty?
			u, (e, d) = h.del_min
			return d if yield(u, dist)
			dist[u] = d
			each_out_connection_of(u){|v, l|
				d = dist[u] + l
				e = d + a_star_heuristic(v)
				if reached.include?(v)
					h.update_key(v, [e, d])
				else
					h.add(v, [e, d])
					reached << v
				end
			}
		end
		block_given? ? nil : dist
	end

	#make_variations :bidir_dijkstra

	def prim(start)
		h = Heap.new
		h.add(start, 0)
		reached = Set[start]
		tree_len = 0

		until h.empty?
			u, key = h.del_min
			tree_len += key

			each_out_connection_of(u){|v, d|
				if reached.include?(v)
					h.update_key(v, d)
				else
					h.add(v, d)
					reached << v
				end
			}
		end
		tree_len
	end

	def each_layer_from(start)
		raise "start must be Enumerable" if !start.kind_of?(Enumerable)
		return enum_for(__method__, start) unless block_given?
		reached = Set[*start]
		current_layer = start

		loop {
			yield current_layer
			next_layer = []
			current_layer.each{|u|
				each_out_connection_of(u){|v|
					next if reached.include?(v)
					reached << v
					next_layer << v
				}
			}	

			return if next_layer.empty?
			current_layer = next_layer
		}
	end
end

class Graph
	include Graphical

	def initialize(*options)
		@options = Set[*options]
	end

	def add_node(property = {})
		Node.new(property)
	end

	def add_edge(u, v, property = {})
		e = Edge.new(u, v, property)
		u.add_edge(e)
		v.add_edge(e)
		e
	end
	
	def del_edge(e)
		u, v = e.opposite.keys
		u.del_edge(e)
		v.del_edge(e)
		e
	end

	class Node
		def initialize(property)
			@property = property
			@edges = Set.new
		end

		def add_edge(e)
			@edges << e
		end

		def del_edge(e)
			@edges.delete(e)
		end

		def to_s
			@property[:name] || super
		end

		def each_edge
			@edges.each{|e| 
				yield e
			}
		end

		attr_reader :property
	end

	class Edge
		def initialize(u, v, property)
			@opposite = {u => v, v => u}
			@property = property
		end
		attr_reader :opposite, :property

		def to_s
			@property[:name] || super
		end

		def length
			@property[:length] || 1
		end
	end

	def each_out_connection_of(u)
		u.each_edge{|e|
			yield(e.opposite[u], e.length)
		}
	end

	alias :each_in_connection_of :each_out_connection_of
end

class Knapsack
	def initialize(items, budget)
		@items = items
		@budget = budget
		@states = []
	end

	def solve
		@items.sort_by!{|c, v| -v.to_f / c}
		@left_value = 0
		@left_cost = 0
		i = 0
		while i < @items.size
			c, v = @items[i]
			break if @left_cost + c > @budget
			@left_cost += c
			@left_value += v
			i += 1
		end

		@l = @r = i
		@lower_bound = @left_value

		return @left_value if @left_cost == @budget || @l == @items.size || @items.size == 1

		@states << [@left_cost, @left_value]
		@states << [@left_cost + @items[@l][0], @left_value + @items[@l][1]]
		@states
	
		loop {
			if @r < @items.size - 1
				@r += 1
				added = @items[@r]
				@states += @states.map{|c, v| [c + added[0], v + added[1]]}
				update_lower_bound
				prun
				break if @states.empty?
			end
	
			if @l > 0
				@l -= 1
				removed = @items[@l]
				@left_cost -= removed[0]
				@left_value -= removed[1]
				@states += @states.map{|c, v| [c - removed[0], v - removed[1]]}
				update_lower_bound
				prun
				break if @states.empty?
			end
		}
	
		return @lower_bound
	end

private
	def upper_bound(cost, value)
		if cost <= @budget
			@r == @items.size-1 ?
			value : value + (@budget - cost).to_f * @items[@r+1][1] / @items[@r+1][0] else
			@l == 0 ?
			value :
			value + (@budget - cost).to_f * @items[@l-1][1] / @items[@l-1][0]
		end
	end

	def prun
		@states.reject!{|c, v|
			next true if c - @left_cost > @budget
			next true if upper_bound(c, v) < @lower_bound+1
			false
		}
		hash = Hash.new(0)
		@states.each{|c, v|
			hash[c] = v if v > hash[c]
		}
		@states = hash.to_a
	end

	def update_lower_bound
		@states.each{|c, v|	
			@lower_bound = v if c <= @budget && v > @lower_bound
		}
	end
end

def knapsack_core(items, budget)
	k = Knapsack.new(items, budget)
	k.solve
end

def knapsack(items, budget)
	table = (0..1).map{ Array.new(budget+1, 0) }
	for i in 0..items.size-1
		p i
		c, v = items[i]
		for j in 0..budget
			x = table[0][j]
			y = (j >= c ? table[0][j-c] + v : 0)
			table[1][j] = x > y ? x : y
		end
		table << table.shift
	end
	table[0][budget]
end

def knapsack_preprocess(items, budget)
	cost_group = items.group_by(&:first)
	items = cost_group.map{|c, group|
		group.sort_by(&:last).last(budget / c)
	}.inject([], &:+)
end

n, m = gets.split.map &:to_i

g = Graph.new
nodes = (0..n).map{g.add_node}
m.times {
	i, j = gets.split.map &:to_i
	g.add_edge(nodes[i], nodes[j])
}

diffs = []
color = {}

(1..n).each{|i|
	u = nodes[i]
	next if color[u]
	color[u] = 0
	count = [0, 0]

	queue = [u]
	until queue.empty?
		u = queue.shift
		c = color[u]
		count[c] += 1
		g.each_out_connection_of(u){|v|
			if color[v] == c
				puts -1
				exit
			end
			next if color[v] 
			color[v] = 1 - c
			queue << v
		}
	end
	diff = -count.sort.inject(:-)
	diffs << diff unless diff == 0
}

total = diffs.inject(:+)
items = diffs.map{|x| [x, x]}
d = total/2 - knapsack_core(knapsack_preprocess(items, total/2), total/2)
x = n / 2 - d
p x * (n - x) - m

Measured memory_bytes: 163836