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:
bracket = input()
stack = []
bracketType = {
	'[': (0, ']'),
	'(': (0, ')'),
	'<': (0, '>'),
	'{': (0, '}'),
	']': (1,),
	')': (1,),
	'>': (1,),
	'}': (1,)
}
res = 0

for b in bracket:
	if bracketType.get(b) == None:
	  break
	elif bracketType.get(b)[0] == 0:
		stack.append(b)
	elif bracketType.get(b)[0] == 1:
		if len(stack) == 0:
			res = 'Impossible'
			break
		else:
			if b != bracketType[stack.pop()][1]:
				res += 1

if len(stack):
	print('Impossible')
else:
	print(res)