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 PYTHON):

Solution:
import fileinput

def get_input():
    inp = fileinput.input()
    s = inp.readline().strip()
    return s


def main():
    s = get_input()
    c = 0
    m = {'<': '>', '{': '}', '[': ']', '(': ')'}
    ope = set(m.keys())
    stack = []
    imp = False
    for let in s:
        if let in ope:
            stack.append(let)
            continue
        else:
            if not stack:
                imp = True
                break
            l = stack.pop()
            r = let
            if m[l] != r:
                c += 1
    if stack:
        imp = True

    if not imp:
        print c
    else:
        print 'Impossible'


if __name__ == '__main__':
    main()