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:
a = raw_input()

opener = 0
closer = 0
openers = []
n = len(a)

sqare = '[]{}<>()'

ans = 0
x = 0

for i in xrange(n):
    if a[i] in '{[(<':
        opener += 1
        openers.append(a[i])
    else:
        closer += 1
        if len(openers) == 0:
            x = 1
            print 'Impossible'
            break
        c = openers.pop()
        v = c + a[i]
        if not (v in sqare):
            ans += 1
        
if opener != closer and x == 0:
    print 'Impossible'
elif opener == closer and x == 0:
    print ans