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 process(S):
    flip = {'(': ')', '[': ']', '{': '}', '<': '>'}
    other = {flip[x]: x for x in flip}
    for x in other:
        flip[x] = other[x]
    d = []
    answer = 0
    for x in S:
        if x in '([{<':
            d.append(x)
        else:
            if len(d)==0:
                return [False, 0]
            x2 = flip[x]
            if x2!=d[-1]:
                answer+=1
            d.pop()
    if len(d)==0:
        return [True, answer]
    else:
        return [False, 0]
    
S = input()
a1, a2 = process(S)
if a1:
    print(a2)
else:
    print('Impossible')