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()
sc = s
sc = sc.replace('<', '(').replace('[', '(').replace('{', '(')
sc = sc.replace('>', ')').replace(']', ')').replace('}', ')')
def chec(ss):
    c = 0
    for i in ss:
        if i == '(':
            c += 1
        if i == ')':
            c -= 1
        if c < 0:
            return False
    return c == 0
if chec(sc):
    l = []
    ans = 0
    for i in s:
        if i in '({[<':
            l.append(i)
        else:
            if i == ')':
                if l[-1] in '{[<':
                    ans += 1
            if i == '}':
                if l[-1] in '([<':
                    ans += 1
            if i == ']':
                if l[-1] in '{(<':
                    ans += 1
            if i == '>':
                if l[-1] in '{[(':
                    ans += 1
            l.pop()
    print(ans)
else:
    print("Impossible")