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:
def opposto(s):
    if s == ")":
        return "("
    elif s == "]":
        return "["
    elif s == "}":
        return "{"
    else:
        return "<"

def f(s):
    n = [0] * 10**6
    checker = 0
    cont = 0
    pos = 0
    for c in s:
        if c in ['(', '[', '{', '<']:
            n[checker] = c
            checker += 1
            pos += 1
        else:
            if checker == 0:
                return "Impossible"
            elif n[checker - 1] == opposto(c):
                checker -= 1
            else:
                checker -= 1
                cont += 1
    if pos == len(s) - pos:
        return cont
    else:
        return "Impossible"
s = str(input())
print(f(s))