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:
try:
    def ad(expr): 
        stack = [] 
        l=0
        for char in expr: 
            if char in ["(", "{", "[","<"]: 
                stack.append(char) 
            else: 
                if not stack: 
                    return 'Impossible'
                current_char = stack.pop() 
                if current_char == '(': 
                    if char != ")" and char=='}' or char==']' or char=='>': 
                        l+=1
                if current_char == '{': 
                    if char != "}" and char==')' or char==']' or char=='>': 
                        l+=1
                if current_char == '[': 
                    if char != "]" and char=='}' or char==')' or char=='>': 
                        l+=1
                if current_char == '<': 
                    if char != ">" and char=='}' or char==')' or char==']': 
                        l+=1
                    
                        
        if stack: 
            return 'Impossible'
        return l
    
    
    s=input()
    print(ad(s))
                    
            
        
    
except:
    pass