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 getResult(s):
    if not s:
        return 'Impossible'
    dic={'(':')','[':']','{':'}','<':'>'}
    res=0
    stack=[]    
    for x in list(s):
        if x in dic:
            stack.append(x)
        else:
            if len(stack)==0:
                return 'Impossible'
            else:
                cur=stack.pop()
                if dic[cur]!=x:
                    res+=1                    
    return res if len(stack)==0 else 'Impossible'   
s=input()
print(str(getResult(s)))