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()
o = "[<{("
c = "]>})"


stack = []
ans = 0


def match(l, r):
    if (l + r == "[]") or (l + r == "<>") or (l + r == "{}") or (l + r == "()"):
        return True
    return False


for i in s:
    if not len(stack):
        stack.append(i)
    elif (i in c) and (stack[-1] in o):
        x = stack.pop()
        if not match(x, i):
            ans += 1
    else:
        stack.append(i)

if len(stack):
    print "Impossible"
else:
    print ans