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:

if __name__ == '__main__':
    s = raw_input()
    stack = []

    opening = set(['<', '{', '[', '('])
    closing = set(['>', '}', ']', ')'])
    c_type = dict(zip(['<', '{', '[', '('], ['>', '}', ']', ')']))

    sub = 0
    valid = True
    for c in s:
        if c in opening:
            stack.append(c)
        else:
            if len(stack) == 0:
                valid = False
                break
            else:
                if c != c_type[stack.pop()]:
                    sub += 1

    if stack or valid == False:
        print 'Impossible'
    else:
        print sub