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)
s = []
ans = 0
m = { ">":"<",  "}":"{", ")":"(", "]":"["}
for i in range(len(a)):
	if(a[i] in ["<", "{", "(", "["]):
		s.append(a[i])
	else:
		if(s == []):
			print "Impossible"
			exit(0)
		else:
			k = s.pop()
			if(k == m[a[i]]):
				pass
			else:
				ans+=1
if(s!=[]):
	print "Impossible"
else:

	print ans