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:
#!/usr/bin/env python
def solve():
    s = raw_input()

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

    opened_brackets = []
    changes = 0
    for i, bracket in enumerate(s):
        if bracket in PAIRS:
            opened_brackets.append(i)
        else:
            if opened_brackets:
                open_bracket = s[opened_brackets.pop()]
                if PAIRS[open_bracket] != bracket:
                    changes += 1
            else:
                print 'Impossible'
                return
    if opened_brackets:
        print 'Impossible'
    else:
        print changes

solve()