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:
s = input()

brackets = {
    '<': '>',
    '{': '}',
    '[': ']',
    '(': ')',
}

OPENING = "<{[("
CLOSING = ">}])"


def main(s):
    stack = []
    res = 0
    for c in s:
        if c in OPENING:
            stack.append(c)
        else:
            if stack:
                top = stack.pop()
                if top in OPENING:
                    if brackets[top] != c:
                        res += 1
                    continue
            return 'Impossible'
    return res if not stack else 'Impossible'


print(main(s))