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:
seq = input()
a = []
fl = True
z = 0
for i in seq:
    if i == '<' or i == '[' or i == '{' or i == '(':
        a.append(i)
    elif i == '>':
        if len(a) and a[-1] == '<': a.pop()
        elif len(a) and a[-1] != '<':
            a.pop()
            z += 1
        else:
            fl = False
            break
    elif i == ')':
        if len(a) and a[-1] == '(': a.pop()
        elif len(a) and a[-1] != '(':
            a.pop()
            z += 1
        else:
            fl = False
            break
    elif i == ']':
        if len(a) and a[-1] == '[': a.pop()
        elif len(a) and a[-1] != '[':
            a.pop()
            z += 1
        else:
            fl = False
            break
    elif i == '}':
        if len(a) and a[-1] == '{': a.pop()
        elif len(a) and a[-1] != '{':
            a.pop()
            z += 1
        else:
            fl = False
            break
if len(a): fl = False
if fl: print(z)
else: print('Impossible')