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:
stack = []

def main():
    s = str(input())
    open = list("<{[(")
    close = list(">}])")

    answer = 0

    for e in s:
        if len(stack) == 0:
            if e in open:
                stack.append(e)
            else:
                print("Impossible")
                return
        else:
            top = len(stack) - 1
            if e in open:
                if stack[top] in close:
                    if open.index(e) != close.index(stack[top]):
                        answer += 1

                    stack.pop(top)
                else:
                    stack.append(e)
            else:
                if stack[top] in close:
                    stack.append(e)
                else:
                    if close.index(e) != open.index(stack[top]):
                        answer += 1

                    stack.pop(top)

    if len(stack) != 0:
        print("Impossible")
    else:
        print(answer)

if __name__ == "__main__":
    main()