class Stack(object):
  def __init__(self):
    self.stack=[]
  def isEmpty(self):
    return self.stack==[]
  def push(self,item):
    self.stack.append(item)
  def pop(self):
    if self.isEmpty():
      raise IndexError,'pop from empty stack'
    return self.stack.pop()
  def peek(self):
    return self.stack[-1]
  def size(self):
    return len(self.stack)

def match(i,j):
  opens='([{'
  closes=')]}'
  return opens.index(i)==closes.index(j)
def syntaxChecker(string):
  stack=Stack()
  balanced=True
  for i in string:
    if i in '([{':
      stack.push(i)
    elif i in ')]}':
      if stack.isEmpty():
        balanced=False
        break
      else:
        j=stack.pop()
        if not match(j,i):
          balanced=False
          break
  if not stack.isEmpty():
    balanced=False
  return balanced

def decimal_to_bin(dec):
  stack=Stack()
  cur=dec
  while cur>0:
    a=cur%2
    cur=cur/2
    stack.push(a)
  binstr=''
  while not stack.isEmpty():
    binstr+=str(stack.pop())
  return binstr

def infixtoPostfix(infix):
  a={}
  a['*']=3
  a['/']=3
  a['+']=2
  a['-']=2
  a['(']=1
  stack=Stack()
  post=''
  for i in infix:
    if i not in a and i!=')':
      post+=i
    elif i=='(':
      stack.push(i)
    elif i==')':
      top=stack.pop()
      while top!='(':
        post+=top
        top=stack.pop()
    else:     
      while not stack.isEmpty() and a[i]<=a[stack.peek()]:
        post+=stack.pop()
      stack.push(i)
  while not stack.isEmpty():
    post+=stack.pop()
  return post
          
def postfixExp(postfix):
  stack=Stack()
  postlist=postfix.split()
  for i in postlist:
    if i not in '+-*/':
      stack.push(i)
    else:
      a=stack.pop()
      b=stack.pop()
      result=math(i,b,a)
      stack.push(result)
  return stack.pop()
def math(x,y,z):
  if x=='+':
    return float(y)+float(z)
  if x=='-':
    return float(y)-float(z)
  if x=='*':
    return float(y)*float(z)
  if x=='/':
    return float(y)/float(z)

class Queue(object):
  def __init__(self):
    self.queue=[]
  def isEmpty(self):
    return self.queue==[]
  def enqueue(self,x):
    self.queue.append(x)
  def dequeue(self):
    if self.queue:
      a=self.queue[0]
      self.queue.remove(a)
      return a
    else:
      raise IndexError,'queue is empty'
  def size(self):
    return len(self.queue)