require 'statsample'


def f2(n)
	return n.odd? ? (n * 3 + 1) / 2 : n / 2

end

def f1(n)
	n = (n * 3 + 1) / 2 if (n.odd?)
	n /= 2 if (n.even?)
	return n

end

def dense(w, d)
	w2 = w - 1

	a = (0...w2).to_a
	s = '0' * w2
	(1..(d * w - 1)).map { a.delete_at(rand(a.size)) }.each { |x| s[x, 1] = '1' }
	return ('1' + s).to_i(2)

end

def stat(l)
	l = [0] if (l.empty?)
        t = t2 = 0
        l.each \
        {
		|x|
		t += x
		t2 += x ** 2
        }
        c = l.size
        a = t.to_f / c
        z = t2.to_f / c - a ** 2
        sd = Math.sqrt(z < 0 ? 0 : z)

	return a, sd, l.max.to_f, l.min.to_f
end

def stat2(l, t, n)
	return Hash[[["a#{n}", "sd#{n}", "mx#{n}"], stat(l)[0..2].map { |x| x / t }].transpose]
end

def d(s)
        c = s.split('').select { |x| x == '1' }.size
	d = c.to_f / s.length
        return d

end

def data(n)
	ns = n.to_s(2)
	nl = ns.length
	m = nl / 2

	nsh = ns[0..m]
	nsl = ns[m..-1]

	asdm1 = stat2(ns.split(/0+/).map { |x| x.length }, nl, 1)

	l1 = ns.split(/1+/)

	l1.shift
	asdm0 = stat2(l1.map { |x| x.length }, nl, 0)

	return {'n' => n, 'ns' => ns, 'nl' => nl, 'd' => d(ns), 'dh' => d(nsh), 'dl' => d(nsl)}.merge(asdm1).merge(asdm0)
end

def pair2(n, m)
	n1 = n

	m.times { n = f2(n) }
	x = {0 => data(n1), 1 => data(n)}

	x[1]['wr'] = x[1]['nl'].to_f / x[0]['nl'].to_f
	return x
end

def pair(d, m)
	w = 100
	return(pair2(dense(w, d), m))
end

def dist(m)

	w = 100
	d = 0.0
	c = 50
	l = []
	c.times \
	{
		|i|

		l << pair(i.to_f / (c - 1), m)
	}
#	$stderr.puts("#{l.size} pts")
	return l
end

def sum(l)

	t = 0.0
	l.each { |x| t += x }
	return t
end

def av(l)
	return nil if (l.empty?)
	return sum(l) / l.size
end

def corr(l, y1)

	yp = "#{y1}_p"
	ye = "#{y1}_e"
	xav = av(l.map { |x| x[y1] })
	yav = av(l.map { |x| x[yp] })

	tx = ty = txy = e = 0.0
	m = nil
	l.each \
	{
		|z|

		x = z[y1]
		y = z[yp]

		txy += (x - xav) * (y - yav)
		tx += (x - xav) ** 2
		ty += (y - yav) ** 2

		z[ye] = (x - y)
		e1 = z[ye]
		e += e1
		m = [m, e1.abs].compact.max
	}
	r = txy / (Math.sqrt(tx) * Math.sqrt(ty))
	e /= l.size
	return {'r' => r, 'e_a' => e, 'e_m' => m}

end

def dot(x, z)

	t = z['c']

	(z.keys - ['c']).each { |v| t += z[v] * x[v] }
	return t

end

def predict(l, vy, z)
	l.each \
	{
		|x|

		x[1]["#{vy}_p"] = dot(x[0], z)
	}
end

def fit(l, vx, vy)

	a = {}

	vx.each { |v| a[v] = l.map { |x| x[0][v] }.to_vector() }

	a[vy] = l.map { |x| x[1][vy] }.to_vector()

	ds = a.to_dataset()

	r = Statsample::Regression.multiple(ds, vy)
#	$stderr.puts(r.summary)

	z = r.coeffs.merge({'c' => r.constant})

	predict(l, vy, z)

	a = corr(l.map { |x| x[1] }, vy)

	return z.merge!(a)

end

def fmt(a)
	a2 = {}
	a.each \
	{
		|k, v|
		a2[k] = v.is_a?(Numeric) ? sprintf("%.3g", v).to_f : v
	}
	return a2

end

def fit1(v, x, l)
	a = fit(l, v, x)
	l1 = l.map { |y| y[1][x] }

	a.merge!({'mn' => l1.min, 'mx' => l1.max})

#	$stderr.puts(fmt({'x' => x}.merge(a.select { |k, v| ['r', 'e_m', 'e_a', 'mn', 'mx'].member?(k) })).inspect)
	return a
end

def model(a)

	(a['v'] + ['wr']).each \
	{
		|x|
		a[x] = fit1(a['v'], x, a['l'])
	}

#	$stderr.puts
	return a

end

def out(fn, a)

	return if (fn.nil?)
	f = File.open(fn, 'a')
	f.puts(a.keys.join("\t")) if (f.size == 0)
	if (a.nil?)
		f.puts
	else
		f.puts(a.values.join("\t"))
	end
	f.close
end

def count(m)
	a = {'l' => dist(m), 'v' => ['a1', 'a0', 'dh', 'dl', 'sd0', 'sd1', 'mx1']}

	a = model(a)
	return a
end

def opt(m, a)
	l = []

	a['l'].size.times \
	{
		|i|
		l << {'ns' => a['l'][i][0]['ns'], 'wr_e' => a['l'][i][1]['wr_e']}
	}

	c = 20
	w = 100
	1000.times \
	{
		|n|

		c = l.size / 4
		l.sort_by! { |x| x['wr_e'] }
#		l.reverse!

		x = rand(c)
		y = rand(c)
		y += 1 if (y == x)
		ns = ns1 = ns2 = nil
		case rand(3)
			when 0
				ns1 = l[x]['ns']
				ns = ns1.dup
				i = rand(w - 1) + 1
				ns[i, 1] = (ns1[i, 1].to_i ^ 1).to_s
			when 1
				ns1 = l[x]['ns']
				ns2 = l[y]['ns']
				ns = ''
				w.times \
				{
					|i|
					ns[i, 1] = [ns1[i, 1], ns2[i, 1]][rand(2)]
				}

			when 2
				ns1 = l[x]['ns']
				ns2 = l[y]['ns']
				i = rand(w)
				ns = ns1[0...i] + ns2[i..-1]
		end

		w2 = ns.to_i(2).to_s(2).length
		raise if (w2 != w)

		next if (l.map { |x| x['ns'] }.member?(ns))

		x = pair2(ns.to_i(2), m)


		(a['v'] + ['wr']).each \
		{
			|vy|
			z = a[vy].select { |k, v| (a['v'] + ['c']).member?(k) }

			predict([x], vy, z)
			corr([x[1]], vy)
		}

		l.pop if (l.size > 2000)
		l << {'ns'=> ns, 'wr_e' => x[1]['wr_e']}

#		puts([l[0]['wr_e'], l[-1]['wr_e'], d(ns), ns].join("\t")) if (n % 40 == 0)
		$stdout.flush
	}
	return l.first
end

def detect(x1, a, j, l)

	x1 = x1.dup
	i = 0
	c = 500
	x1['nl'] = 1
	loop \
	{
		x2 = {}
		(a['v'] + ['wr']).each \
		{
			|vy|

			x2[vy] = dot(x1, a[vy].select { |k, x| (a['v'] + ['c']).member?(k) })

			x2[vy] += l[j][1]["#{vy}_e"] if (!j.nil?)

			x2[vy] = a[vy]['mn'] if (x2[vy] < a[vy]['mn'])
			x2[vy] = a[vy]['mx'] if (x2[vy] > a[vy]['mx'])
		}
		x2['nl'] = x1['nl'] * x2['wr']
		x1 = x2
		i += 1
		break if (x1['nl'] < 1 || i == c)
	}
	return i == c ? nil : i

end

def count2(l, a, y)

	t2 = 0
	l.size.times \
	{
		|i|
		t2 += 1 if (detect(l[i][0], a, nil, l).nil?)
	}

	t = 0
	l.size.times \
	{
		|i|
		l1 = []
		l.size.times \
		{
			|j|
			x = detect(l[i][0], a, j, l)
			l1 << j if (x.nil?)
		}
		t += l1.size
		$stderr.puts([i, t, l1].inspect)
	}
	return {"t#{y}" => t, "t#{y}2" => t2}
end

def stat1(l)
	return Hash[[['a', 'sd', 'mx', 'mn'], stat(l)].transpose]
end

def test(m, a)
	l = dist(m)

	(a['v'] + ['wr']).each \
	{
		|vy|
		z = a[vy].select { |k, v| (a['v'] + ['c']).member?(k) }

		predict(l, vy, z)
		corr(l.map { |x| x[1] }, vy)
	}
	return count2(l, a, 'b')
end

def load()
	x = Kernel.eval(File.open('out.txt').readlines[0])
	p(x)
	exit
end

load() if (File.exists?('out.txt'))

srand(0)


m = [ARGV[0], 50].compact.first.to_i
a = count(m)

File.open(fn = 'out1.txt', 'w').close

200.times \
{
	|i|
	x = opt(m, a)

	j = (0...a['l'].size).max_by { |x| a['l'][x][1]['wr_e'] }

	a['l'][j] = pair2(x['ns'].to_i(2), m)

	a = model(a)
	if (i % 5 == 0) then
		x = stat1(a['l'].map { |x| x[1]['wr_e'] }).merge(count2(a['l'], a, 'a')).merge(test(m, a))
		out(fn, x)
		break if (x['tb'] == 0)
	end
}

f = File.open('out.txt', 'w')
f.puts(a.inspect)
f.close