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 PYTHON3):

Solution:
def main( s: str):
    if len(s)==0 or len(s)%2!=0: 
        return 'Impossible'
    leftchr =['(','{','<','[']
    stack = list()
    opdict = {'(':')','{':'}','<':'>','[':']'}
    mix=0
    for oper in s:
        if oper in leftchr:
            stack.append(oper)
        else:
            try: 
                top = stack.pop()
            except :
                return 'Impossible' 
            if opdict.get(top)!=oper: 
               mix+=1
    if len(stack)!=0:
         return 'Impossible' 
    return mix
s=str(input())
print(main(s))