The time was 3xxx, and the highly developed civilization was in a stagnation period. Historians decided to learn the wisdom of the past in an attempt to overcome this situation. What I paid attention to was the material left by the genius of the early days of computers. The calculation formula is written in this material and I would like to know the calculation result, but unfortunately some of the characters are fading and cannot be read. Since there is no help for it, I decided to find the largest possible number as a calculation result. The calculation formula is written in binary numbers, and there are three types of operations: addition, subtraction, and multiplication. Parentheses are also used, but the numbers inside the parentheses are not the only ones. To be exact, it is necessary to satisfy the grammar defined by the following BNF.


<expression> :: = <number> | <expression> <operation> <expression>
| (<expression> <operation> <expression>)
<number> :: = <digit> | <number> <digit>
<operation> :: = + |-| *
<digit> :: = 0 | 1


Due to the limited computing power of computers at that time, numbers are integers between 0 and 210 and do not go out of this range during calculations. However, the calculation is done in parentheses first, and the multiplication is done before addition / subtraction. In other cases, the calculation is performed in order from the left.

Constraints

* Formulas must be between 1 and 100 characters
* All characters except line breaks are either 01 +-* ().
*. Number is 5 or less

Input

The input consists of one line and is given one formula to decipher. The formula is 1 to 100 characters. Up to 5 characters cannot be read for one formula and are represented by ".". The characters contained in the given formula are either 01 +-* ().

Output

Find the one that maximizes the calculation result among the original formulas, and output the calculation result in decimal notation. Output -1 if you can't make what you think is the original formula no matter how you fill in the unreadable characters.

Examples

Input

000


Output

0


Input

0.0


Output

2


Input

...


Output

7


Input

(1.1)


Output

2


Input

0-1.


Output

-1

Difficulty: UNKNOWN_DIFFICULTY

Starter code:

Solutions:
from itertools import product
import time

def ok(s):
	if '(+' in s or '(-' in s or '(*' in s or ('++' in s) or ('+-' in s) or ('-+' in s) or ('--' in s) or ('**' in s) or ('*+' in s) or ('*-' in s):
		return False
	if '(' in s or ')' in s:
		dic = {}
		count = -1
		for c in s:
			if c == '(':
				count += 1
				dic[count] = 0
			elif c == ')':
				if dic[count] == 0:
					return False
				count -= 1
			elif c in '+-*' and count in dic:
				dic[count] += 1
		return True
	else:
		return True

def check(s):
	i = 0
	ans = ''
	tmp = []
	try:
		while i < len(s):
			if s[i] in '01':
				tmp.append(s[i])
			else:
				if len(tmp):
					t = ''.join(tmp)
					t = str(int(t, 2))
					if int(t) >= 1024:
						return -99999999
					ans += t
				ans += s[i]
				tmp = []
			i += 1
		if len(tmp):
			t = ''.join(tmp)
			t = str(int(t, 2))
			ans += t
	except:
		return -99999999
	try:
		if ok(ans):
			xxx = eval(ans)
			if '-' not in ans and xxx < 1024:
				return xxx
			elif '-' in ans and xxx < 1024:
				for i in range(len(ans)):
					if ans[i] == '-':
						mid = i
						(r, l) = (mid - 1, mid + 1)
						count = 0
						while r >= 0:
							if ans[r] == ')':
								count += 1
							elif ans[r] == '(':
								count -= 1
								if count < 0:
									r += 1
									break
							if count == 0 and ans[r] in '+-':
								r += 1
								break
							r -= 1
						r = max(r, 0)
						count = 0
						while l < len(ans):
							if ans[l] == '(':
								count += 1
							elif ans[l] == ')':
								count -= 1
								if count < 0:
									break
							if count == 0 and ans[l] in '+-':
								break
							l += 1
						(a, b) = (eval(ans[r:mid]), eval(ans[mid + 1:l]))
						if a >= 1024 or b >= 1024 or a - b < 0:
							return -99999999
				return xxx
			else:
				return -99999999
		else:
			return -99999999
	except:
		return -99999999
s = input().split('.')
mx = -1
hoge = product('01+-*()', repeat=len(s) - 1)
for table in hoge:
	tmp = s[0]
	i = 1
	for c in table:
		tmp += c + s[i]
		i += 1
	mx = max(mx, check(tmp))
print(mx)


from collections import defaultdict
from collections import deque
from heapq import heappush, heappop
import sys
import math
import bisect
import random

def LI():
	return list(map(int, sys.stdin.readline().split()))

def I():
	return int(sys.stdin.readline())

def LS():
	return list(map(list, sys.stdin.readline().split()))

def S():
	return list(sys.stdin.readline())[:-1]

def IR(n):
	l = [None for i in range(n)]
	for i in range(n):
		l[i] = I()
	return l

def LIR(n):
	l = [None for i in range(n)]
	for i in range(n):
		l[i] = LI()
	return l

def SR(n):
	l = [None for i in range(n)]
	for i in range(n):
		l[i] = S()
	return l

def LSR(n):
	l = [None for i in range(n)]
	for i in range(n):
		l[i] = LS()
	return l
sys.setrecursionlimit(1000000)
mod = 1000000007

def A():
	e = LI()
	d = defaultdict(int)
	for i in e:
		d[i] += 1
	for i in d.values():
		if i != 2:
			print('no')
			break
	else:
		print('yes')
	return

def B():
	n = I()
	a = LI()
	a.sort()
	ans = -float('inf')
	for c in range(n):
		for d in range(c):
			m = a[c] - a[d]
			for i in range(n)[::-1]:
				if i != c and i != d:
					e = i
					break
			for i in range(e)[::-1]:
				if i != c and i != d:
					b = i
					break
			ans = max(ans, (a[e] + a[b]) / m)
	print(ans)
	return

def C():

	def gcd(a, b):
		if a == 0:
			return b
		return gcd(b % a, a)
	s = input()
	n = len(s)
	if s.count('(') == 0:
		s = float(s)
		b = 10 ** (n - 2)
		a = round(s * b)
		g = gcd(a, b)
		a //= g
		b //= g
	else:
		n = s.find('(')
		t = float(s[:n])
		b = 10 ** (n - 2)
		a = round(t * b)
		g = gcd(a, b)
		a //= g
		b //= g
		l = s.find('(') - s.find('.') - 1
		s = s[n + 1:-1]
		m = len(s)
		c = round(float(s))
		d = (10 ** m - 1) * 10 ** l
		g = gcd(c, d)
		c //= g
		d //= g
		a = a * d + b * c
		b = b * d
		g = gcd(a, b)
		a //= g
		b //= g
	print(str(a) + '/' + str(b))
	return

def D():
	return

def E():

	def dfs(d, k, s):
		if d == n:
			ans.append(k)
		else:
			b = [block[d][i] for i in range(8)]
			if sum(b[:4]) == 0:
				b = b[4:] + [0, 0, 0, 0]
			dfs(d + 1, *check(b, k, s))
			if not b[0] | b[1] | b[4] | b[5]:
				b_ = [b[2], b[3], 0, 0, b[6], b[7], 0, 0]
				if sum(b_):
					dfs(d + 1, *check(b_, k, s))
			if not b[1] | b[3] | b[5] | b[7]:
				b_ = [0, b[0], 0, b[2], 0, b[4], 0, b[6]]
				if sum(b_):
					dfs(d + 1, *check(b_, k, s))
			if not b[2] | b[3] | b[6] | b[7]:
				b_ = [0, 0, b[0], b[1], 0, 0, b[4], b[5]]
				if sum(b_):
					dfs(d + 1, *check(b_, k, s))
			if not b[0] | b[2] | b[4] | b[6]:
				b_ = [b[1], 0, b[3], 0, b[5], 0, b[7], 0]
				if sum(b_):
					dfs(d + 1, *check(b_, k, s))
			if not b[1] | b[2] | b[3] | b[5] | b[6] | b[7]:
				b_ = [0, 0, 0, b[0], 0, 0, 0, b[4]]
				if sum(b_):
					dfs(d + 1, *check(b_, k, s))
			if not b[0] | b[2] | b[3] | b[4] | b[6] | b[7]:
				b_ = [0, 0, b[1], 0, 0, 0, b[5], 0]
				if sum(b_):
					dfs(d + 1, *check(b_, k, s))
			if not b[0] | b[1] | b[3] | b[4] | b[5] | b[7]:
				b_ = [0, b[2], 0, b[6], 0, 0, 0, 0]
				if sum(b_):
					dfs(d + 1, *check(b_, k, s))
			if not b[0] | b[1] | b[2] | b[4] | b[5] | b[6]:
				b_ = [b[3], 0, 0, 0, b[7], 0, 0, 0]
				if sum(b_):
					dfs(d + 1, *check(b_, k, s))

	def check(b, k, s):
		i = 19
		k_ = k
		s_ = [[s[i][j] for j in range(4)] for i in range(20)]
		while i >= 1 and (not b[0] & s[i - 1][0] | b[1] & s[i - 1][1] | b[2] & s[i - 1][2] | b[3] & s[i - 1][3] | b[4] & s[i][0] | b[5] & s[i][1] | b[6] & s[i][2] | b[7] & s[i][3]):
			i -= 1
		s_[i] = [s_[i][j] + b[j] for j in range(4)]
		s_[i + 1] = [s_[i + 1][j] + b[j + 4] for j in range(4)]
		i = 0
		while i < 20:
			if sum(s_[i]) == 4:
				k_ += 1
				for j in range(i, 19):
					s_[j] = [s_[j + 1][l] for l in range(4)]
				s_[19] = [0, 0, 0, 0]
				i -= 1
			i += 1
		return (k_, s_)
	while 1:
		(h, n) = LI()
		if h == n == 0:
			break
		s = [[0, 0, 0, 0] for i in range(20)]
		for i in range(h):
			c = S()
			c += S()
			s[i] = [1 if c[j] == '#' else 0 for j in range(4)]
		block = [[0, 0, 0, 0, 0, 0, 0, 0] for i in range(n)]
		for i in range(n):
			b = S()
			b += S()
			b += S()
			b += S()
			block[i] = [1 if b[j] == '#' else 0 for j in range(8)]
		ans = []
		dfs(0, 0, s)
		print(max(ans))
	return

def F():

	def dfs(d, k):
		if d == len(s):
			t.append(k)
		elif s[d] == '.':
			for i in range(2):
				dfs(d + 1, k + [str(i)])
			for i in '+-*()':
				dfs(d + 1, k + [i])
		else:
			dfs(d + 1, k + [s[d]])

	def parse_expr(s, i):
		if i == float('inf'):
			return (-1, float('inf'))
		f = s[i - 1] == '('
		k = 0
		(t, i, k) = parse_term(s, i, k)
		while i < len(s) and s[i] in '+-':
			k += 1
			(op, i) = parse_op(s, i)
			(t_, i, k) = parse_term(s, i, k)
			t = calc(op, t, t_)
			if t >= 1024 or t < 0:
				return (-1, float('inf'))
		if f and (not k):
			return (-1, float('inf'))
		return (t, i)

	def parse_term(s, i, k):
		(f, i) = parse_factor(s, i)
		while i < len(s) and s[i] == '*':
			k += 1
			(op, i) = parse_op(s, i)
			(f_, i) = parse_factor(s, i)
			f = calc(op, f, f_)
			if f >= 1024 or f < 0:
				return (-1, float('inf'), k)
		return (f, i, k)

	def parse_op(s, i):
		return (s[i], i + 1)

	def parse_factor(s, i):
		if i >= len(s):
			return (-1, float('inf'))
		if s[i] == '(':
			i += 1
			(e, i) = parse_expr(s, i)
			if i >= len(s) or s[i] != ')':
				return (-1, float('inf'))
			i += 1
			return (e, i)
		else:
			if not s[i].isdecimal():
				return (-1, float('inf'))
			n = int(s[i])
			i += 1
			while i < len(s) and s[i].isdecimal():
				n *= 2
				n += int(s[i])
				i += 1
			if n >= 1024 or n < 0:
				return (-1, float('inf'))
			return (n, i)

	def calc(op, a, b):
		if op == '+':
			return a + b
		elif op == '-':
			return a - b
		elif op == '*':
			return a * b
	s = S()
	f = defaultdict(lambda : 0)
	for i in range(2):
		f[str(i)] += 1
	t = []
	dfs(0, [])
	ans = -1
	for s in t:
		(e, i) = parse_expr(s, 0)
		if i == len(s):
			ans = max(ans, e)
	print(ans)
	return

def G():
	return

def H():
	return

def I_():
	return

def J():
	return
F()


import math, string, itertools, fractions, heapq, collections, re, array, bisect, sys, random, time, copy, functools
sys.setrecursionlimit(10 ** 7)
inf = 10 ** 20
eps = 1.0 / 10 ** 13
mod = 10 ** 9 + 7
dd = [(-1, 0), (0, 1), (1, 0), (0, -1)]
ddn = [(-1, 0), (-1, 1), (0, 1), (1, 1), (1, 0), (1, -1), (0, -1), (-1, -1)]

def LI():
	return [int(x) for x in sys.stdin.readline().split()]

def LI_():
	return [int(x) - 1 for x in sys.stdin.readline().split()]

def LF():
	return [float(x) for x in sys.stdin.readline().split()]

def LS():
	return sys.stdin.readline().split()

def I():
	return int(sys.stdin.readline())

def F():
	return float(sys.stdin.readline())

def S():
	return input()

def pf(s):
	return print(s, flush=True)

def main():
	rr = []

	def f(s):
		ca = '01+-*()'
		sa = s.split('.')
		r = -1
		sl = len(sa)
		fm = {}

		def _f(s):
			if s in fm:
				return fm[s]
			if ')' in s:
				ri = s.index(')')
				if len(s) > ri + 1 and s[ri + 1] in '01':
					fm[s] = -1
					return -1
				li = -1
				for i in range(ri - 1, -1, -1):
					if s[i] == '(':
						li = i
						break
				if li < 0 or (li > 0 and s[li - 1] in '01'):
					fm[s] = -1
					return -1
				ts = s[li + 1:ri]
				if '+' not in ts and '-' not in ts and ('*' not in ts):
					fm[s] = -1
					return -1
				tr = _f(ts)
				if tr == -1:
					fm[s] = -1
					return -1
				fm[s] = _f(s[:li] + tr + s[ri + 1:])
				return fm[s]
			if '(' in s:
				fm[s] = -1
				return -1
			l = len(s)
			if '*' in s:
				oi = s.index('*')
				li = oi
				for i in range(oi - 1, -1, -1):
					if s[i] not in '01':
						break
					li = i
				ri = oi
				for i in range(oi + 1, l):
					if s[i] not in '01':
						break
					ri = i
				if li == oi or ri == oi:
					fm[s] = -1
					return -1
				t = int(s[li:oi], 2)
				u = int(s[oi + 1:ri + 1], 2)
				tu = t * u
				if t < 0 or t >= 1024 or u < 0 or (u >= 1024) or (tu < 0) or (tu >= 1024):
					fm[s] = -1
					return -1
				ts = bin(tu)[2:]
				fm[s] = _f(s[:li] + ts + s[ri + 1:])
				return fm[s]
			pi = inf
			mi = inf
			if '+' in s:
				pi = s.index('+')
			if '-' in s:
				mi = s.index('-')
			if pi == inf and mi == inf:
				t = int(s, 2)
				fm[s] = s
				if t < 0 or t >= 1024:
					fm[s] = -1
				return fm[s]
			oi = min(pi, mi)
			li = oi
			for i in range(oi - 1, -1, -1):
				if s[i] not in '01':
					break
				li = i
			ri = oi
			for i in range(oi + 1, l):
				if s[i] not in '01':
					break
				ri = i
			if li == oi or ri == oi:
				fm[s] = -1
				return -1
			t = int(s[li:oi], 2)
			t = int(s[li:oi], 2)
			u = int(s[oi + 1:ri + 1], 2)
			tu = t + u
			if oi == mi:
				tu = t - u
			if t < 0 or t >= 1024 or u < 0 or (u >= 1024) or (tu < 0) or (tu >= 1024):
				fm[s] = -1
				return -1
			ts = bin(tu)[2:]
			fm[s] = _f(s[:li] + ts + s[ri + 1:])
			return fm[s]
		for ci in itertools.product(ca, repeat=sl - 1):
			t = ''
			for i in range(len(ci)):
				t += sa[i]
				t += ci[i]
			t += sa[-1]
			tr = _f(t)
			if tr != -1:
				tr = int(tr, 2)
				if tr >= 1024 or tr < 0:
					tr = -1
			if r < tr:
				r = tr
		return r
	while 1:
		n = S()
		if n == 0:
			break
		rr.append(f(n))
		break
	return '\n'.join(map(str, rr))
print(main())