=begin
1: (0)
2: (0,0)
ω: (0,1)
ω*2: (0,1,0,1)
ω^2: (0,1,1)
ω^ω: (0,1,2)
ω^(ω*2): (0,1,2,1,2)
ω^ω^2: (0,1,2,2)
ω^ω^ω: (0,1,2,3)

ja: http://ja.googology.wikia.com/wiki/%E5%8E%9F%E5%A7%8B%E6%95%B0%E5%88%97%E6%95%B0
en: http://googology.wikia.com/wiki/User_blog:Kyodaisuu/A_program_of_Kirby-Paris_hydra
=end

class Priseq 
	def self.[] *m;new *m end
	attr_reader :m
	def initialize *m;@m = m end
	def succ;Primat[*@m,0] end
	def succ?;@m.last===@m.min end
	def zero?;@m.size===0 end
	def === x;min=@m.min;return @m===x.m.map{|a|a-min} if x.is_a? Priseq;false end
	def pred;return Priseq[*@m[0..-2]] if succ?;self end
	def < x
		if x.is_a? Priseq
			min = @m.min
			m = x.m.map{|c|c-min}
			r = @m.each_with_index do |a,i|
				b = m[i]
				return false unless b
				return true if a<b
			end
			return false if r==@m
			return r
		end
		false
	end
	def > x
		if x.is_a? Priseq
			min = @m.min
			m = x.m.map{|c|c-min}
			r = m.each_with_index do |a,i|
				b = @m[i]
				return false unless b
				return true if a<b
			end
			return false if r==m
			return r
		end
		true
	end
	def >= x;!(self<x) end
	def <= x;!(self>x) end
	def + x
		return Priseq[*(self<x ? x.m+@m : @m+x.m)] if x.is_a?
		Priseq[*@m, *([0]*x.to_i)]
	end
	def to_s;'('+@m.join(',')+')' end
	def [] n
		min = @m.min
		i = @m.rindex{|a|a>min}
		a = @m[i]
		r = Priseq[*@m]; m = r.m
		j = m[0,i].rindex{|b|b<a}
		m.delete_at i
		m.insert j, *(m.slice!(j,i-j) * n)
		return m.size if m.all?{|c|min===c}
		r
	end
end
def Priseq *m;Priseq.new *m end
class Integer;def succ?;self>0 end end

#Slow-growing hierarchy
def g(a,n)
	return 0 if a.zero?
	return g(a.pred,n)+1 if a.succ?
	g(a[n],n)
end

#Hardy hierarchy
def H(a,n)
	return n if a.zero?
	return g(a.pred,n+1) if a.succ?
	H(a[n],n)
end

#Fast-growing hierarchy
def f(a,n)
	return n+1 if a.zero?
	if a.succ?
		r = n; b = a.pred
		n.to_i.times{ r = f(b,r) }
		return r
	end
	f(a[n],n)
end