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:
opening = set(['(','<','[','{'])
closing = set([')','>',']','}'])
 
def im_noob(s):
    ans = 0
    l = 0
    stack = []
    for i in s:
        if i in opening:
            if i == '[':
                stack.append(']')
 
            elif i == '<':
                stack.append('>')
 
            elif i == '{':
                stack.append('}')
            
            elif i == '(':
                stack.append(')')
            l+=1
        else:
            try:
                if i!=stack[l-1]:
                    ans+=1
                    stack.pop()
                    l-=1
                else:
                    stack.pop()
                    l-=1
            except:
                return "Impossible"
    
    if l>0:
        return "Impossible"
 
    return ans

 
s = input()
print(im_noob(s))