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 stacks(brackets):
    opening = ['[', '{', '(', '<']
    closing = ['}', '{', '(', '<']
    stack = []
    changes = 0
    for b in brackets:
        if b in opening:
            stack.append(b)
        else:
            if len(stack) == 0:
                return -1
            last_brackets = stack.pop()
            if b == ']':
                if last_brackets != '[':
                    changes += 1
            elif b == '}':
                if last_brackets != '{':
                    changes += 1
            elif b == ')':
                if last_brackets != '(':
                    changes += 1
            elif b == '>':
                if last_brackets != '<':
                    changes += 1
            else:
                return -1
    if stack:
        return -1
    else:
        return changes


if __name__ == "__main__":
    _in = input()
    brackets = []
    for b in _in:
        brackets.append(str(b))
    v = stacks(brackets)
    if v == -1:
        print("Impossible")
    else:
        print(v)