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 PYTHON):

Solution:
s=raw_input()
op=["<","(","{","["]
cl=[">",")","}","]"]
d={op[i]:i for i in xrange(4)}
for i in xrange(4):
    d[cl[i]]=i
rem=0
flag=True
for i in s:
    if i in cl:
        rem-=1 
        if rem<0:
            flag=False
            break
    elif i in op:
        rem+=1 
stack=[]
if rem!=0 or not flag:
    print "Impossible"
else:
    ans=0
    
    for i in s:
        if i in cl:
            if d[i]!=d[stack[-1]]:
                ans+=1 
            stack.pop()
        if i in op:
            stack.append(i)
    print ans