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()
a = list(a)

stack = []
rep = 0
braces = {}
braces['<'] = '>'
braces['('] = ')'
braces['['] = ']'
braces['{'] = '}'

openb = braces.keys()
closeb = braces.values()
for i in a:
	if i in openb:
		stack.append(i)
	elif len(stack) == 0 and i in closeb:
		print "Impossible"
		exit()
	elif i in closeb:
		if braces[stack[len(stack) - 1]] != i:
			rep += 1
		stack.pop()
if len(stack) == 0:
	print rep
else:
	print 'Impossible'