require 'set'

class Graph
	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

# def get_path(s, t, reached = Set[s])
# 	return [t] if s == t
# 	s.each_edge do |e|
# 		v = e.opposite[s]
# 		next if reached.include?(v)
#
# 		cap = e.property[:capacity]
# 		flow = (e.property[:flow] ||= 0)
# 		to = (e.property[:flow_to] ||= v)
# 		rest = (to == v ? cap - flow : cap + flow)
# 		next if rest <= 0
#
# 		reached << v
# 		if path = get_path(v, t, reached)
# 			return [s, e, *path]
# 		end
# 	end	
# 	return nil
# end

def get_path(s, t)
	reached = Set[s]
	queue = [s]
	comming_edge = {}
	until queue.empty?
		u = queue.shift
		u.each_edge do |e|	
			v = e.opposite[u]
			next if reached.include?(v)

			cap = e.property[:capacity]
			flow = (e.property[:flow] ||= 0)
			to = (e.property[:flow_to] ||= v)
			rest = (to == v ? cap - flow : cap + flow)
			next if rest <= 0

			reached << v
			comming_edge[v] = e
			queue << v

			if v == t
				queue = []
				break
			end
		end	
	end

	if comming_edge[t]
		path = [t]
		v = t
		until path[0] == s
			e = comming_edge[v]
			u = e.opposite[v]
			path = [u, e, *path]
			v = u
		end
		return path
	end
	return nil
end

def compute_min(path)
	m = Float::INFINITY
	i = 0
	while i < path.size - 1
		u = path[i]
		e = path[i+1]
		v = path[i+2]
		cap = e.property[:capacity]
		flow = e.property[:flow]
		to = e.property[:flow_to]
		rest = (to == v ? cap - flow : cap + flow)
		m = rest if rest < m
		i += 2
	end
	m
end

def add_flow(df, path)
	i = 0
	while i < path.size - 1
		u = path[i]
		e = path[i+1]
		v = path[i+2]
		cap = e.property[:capacity]
		flow = e.property[:flow]
		to = e.property[:flow_to]

		if to == v 
			e.property[:flow] += df
		elsif flow >= df
			e.property[:flow] -= df
		else
			e.property[:flow_to] = v
			e.property[:flow] = df - flow
		end
		i += 2
	end
end

def reachable(s, reached = Set[s])
	s.each_edge do |e|
		v = e.opposite[s]
		next if reached.include?(v)

		cap = e.property[:capacity]
		flow = (e.property[:flow] ||= 0)
		to = (e.property[:flow_to] ||= v)
		rest = (to == v ? cap - flow : cap + flow)
		next if rest <= 0

		reached << v
		reachable(v, reached)
	end	
	reached
end

class Poly
	def initialize(s)
		@hash = Hash.new(0)
		s.chomp.split(?+).each do |term|
			if term =~ /((\d+)\*)?x(\*\*(\d+))?/
				@hash[$3 ? $4.to_i : 1] = ($2 ? $1.to_i : 1)
			else
				@hash[0] = term.to_i
			end
		end
	end

	def +(poly)
		sum = self.class.new("")
		@hash.each {|k, a| sum.hash[k] += a}
		poly.hash.each {|k, a| sum.hash[k] += a}
		sum
	end

	def to_s
		ks = @hash.keys
		ks.delete_if {|k| !@hash[k] || @hash[k] == 0}
		return ?0 if ks.empty?
		ks.sort!
		ks.reverse!	
		ks.map {|k|
			if k == 0
				@hash[k]
			else
				[@hash[k] == 1 ? "" : @hash[k], ?x, k == 1 ? "" : "^#{k}"].join
			end
		}.join(?+)
	end

	attr_reader :hash
end

loop do
	n, m = gets.split.map(&:to_i)	
	break if n == 0
	g = Graph.new
	nodes = (0..n).map { g.add_node }
	edges = []

	x = 1000000000
	m.times do
		i, j, poly = gets.chomp.split
		poly.gsub!(?^, '**')
		poly.gsub!(/\dx/){|s| s[0..-2] + '*x'}
		e = g.add_edge(nodes[i.to_i], nodes[j.to_i])
		e.property[:poly_capacity] = poly
		e.property[:capacity] = eval(poly)
		edges << e
	end

	loop do
		path = get_path(nodes[1], nodes[n])
		break if !path
		min = compute_min(path)	
		add_flow(min, path)
	end

	l_nodes = reachable(nodes[1])
	min_cut = []
	edges.each do |e|
		u, v = e.opposite.keys
		if l_nodes.include?(u) ^ l_nodes.include?(v)
			min_cut << e
		end
	end

	# saturated = edges.select{|e| e.property[:flow] == e.property[:capacity]}
	polys = min_cut.map {|e| Poly.new(e.property[:poly_capacity])}
	puts (polys.inject(:+) || Poly.new(""))

end

Measured memory_bytes: 13192