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:
s = input()
otc = {
    '[': ']',
    '{': '}',
    '(': ')',
    '<': '>'
}

cto = {
    '>': '<',
    '}': '{',
    ')': '(',
    ']': '[',
}
stack = []
res1 = 0
for c in s:
    if c in otc.keys():
        stack.append(c)
        continue

    if len(stack) == 0:
        res1 = -1
        break

    o = stack[len(stack) - 1]
    stack.pop()
    if c == otc[o]:
        continue
    else:
        res1 += 1

if res1 == -1 or len(stack) != 0:
    print("Impossible")

else:
    print(res1)