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:
from collections import deque

s = str(raw_input())
n = len(s)

c1 = 0
c2 = 0
c3 = 0
c4 = 0

r = 0

opening = "<[{("
closing = ">]})"

match = [False] * 255
match[ord('(')] = ')'
match[ord(')')] = '('
match[ord('<')] = '>'
match[ord('>')] = '<'
match[ord('[')] = ']'
match[ord(']')] = '['
match[ord('{')] = '}'
match[ord('}')] = '{'

stack = deque()

r = 0
for c in s:
    if c in opening:
        stack.append(c)
    else:
        if not len(stack):
            print "Impossible"
            exit(0)
        old = stack.pop()
        if match[ord(old)] != c:
            r += 1

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