Problem: You are given string s consists of opening and closing brackets of four kinds <>, {}, [], (). There are two types of brackets: opening and closing. You can replace any bracket by another of the same type. For example, you can replace < by the bracket {, but you can't replace it by ) or >.

The following definition of a regular bracket sequence is well-known, so you can be familiar with it.

Let's define a regular bracket sequence (RBS). Empty string is RBS. Let s1 and s2 be a RBS then the strings <s1>s2, {s1}s2, [s1]s2, (s1)s2 are also RBS.

For example the string "[[(){}]<>]" is RBS, but the strings "[)()" and "][()()" are not.

Determine the least number of replaces to make the string s RBS.

Input

The only line contains a non empty string s, consisting of only opening and closing brackets of four kinds. The length of s does not exceed 106.

Output

If it's impossible to get RBS from s print Impossible.

Otherwise print the least number of replaces needed to get RBS from s.

Examples

Input

[&lt;}){}


Output

2

Input

{()}[]


Output

0

Input

]]


Output

Impossible

Solution (in PYTHON):

Solution:
o = ['(', '[', '<', '{']
cl = [')', ']', '>', '}']

def f():
  seq = raw_input()
  v = []
  count = 0

  for c in seq:
    if c in o:
      v.append(c)
    elif c in cl:
      if len(v) is 0:
        print "Impossible"
        return
      x = v.pop()
      m = cl[o.index(x)]
      if c is not m:
        count += 1
  
  if len(v) is 0:
    print count
  else:
    print "Impossible"
  return

f()