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:
import io, os
input = io.StringIO(os.read(0, os.fstat(0).st_size).decode()).readline

stack = []
c=0
opts = {'(':0,')':1,'<':2,'>':3,'[':4,']':5,'{':6,'}':7}
for s in input():
	if s not in opts:break
	v = opts[s]
	if v&1:
		if not stack:
			print("Impossible")
			exit()
		x = stack.pop()
		if x != v: c+=1
	else:
		stack.append(v+1)
if stack:
	print("Impossible")
	exit()
print(c)