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:
s1={'[','{','<','('}
s2={'}',']','>',')'}

f= {'{':'}', '[':']', '(':')', '<':'>'}

s= raw_input()

ctr=0
flag=0

for i in xrange(0, len(s)):
	if ctr<0:
		flag=1
		break
	if s[i]in s1:
		ctr+=1
	else:
		ctr-=1
ret=0		

if ctr != 0 or flag==1:
	print 'Impossible'
else:
	fifo=[]
	for i in xrange(0, len(s)):
		if s[i] in s1:
			fifo.append(s[i])
		else :
			if f[fifo[-1]]!= s[i]:
				ret+=1
			fifo.pop()
	print ret