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:
def quest():
    seq=raw_input()
    l=[]
    counter=0
    rbs=["<","{","[","(",")","]","}",">"]
    for i in range(len(seq)):
        if seq[i] in rbs[0:4]:
            l.append(seq[i])
        else:
            if len(l)!=0:
                if (l[-1]==rbs[0] and seq[i]==rbs[-1]) or (l[-1]==rbs[1] and seq[i]==rbs[-2]) or (l[-1]==rbs[2] and seq[i]==rbs[-3]) or (l[-1]==rbs[3] and seq[i]==rbs[-4]):
                    l.pop()
                else:
                    l.pop()
                    counter+=1
            else:
                print "Impossible"
                return
    if len(l)==0:
        print counter
    else:
        print "Impossible"
        return
quest()