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:
a=input()
s=[]
replacements=0
flag=0
for i in range(len(a)):
    if a[i] in '({[<':
        s.append(a[i])
    else:
        if len(s)==0 :
            flag=1
            break
        top=s.pop()
        if a[i]=='>' and top!='<':
            replacements+=1
        if a[i]==')' and top!='(':
            replacements+=1
        if a[i]==']' and top!='[':
            replacements+=1
        if a[i]=='}' and top!='{':
            replacements+=1
if len(s)>0 or flag==1:
    print("Impossible")
else:
    print(replacements)