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:
s2=input()
dic={'{':1,'}':-1,'<':2,'>':-2,'[':3,']':-3,'(':4,')':-4}
stack=[]
count=0
n=0
for x in s2:
    if dic[x]<0:
        if n==0:
            print("Impossible")
            quit()
        if dic[stack[n-1]]+dic[x]!=0:
            count+=1
        stack.pop()
        n=n-1
    else:
        stack.append(x)
        n=n+1
if n!=0:
    print("Impossible")
else:
    print(count)