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:
def is_left(a):
	return a in ('{', '[', '(', '<')
def is_right(a):
	return a in ('}', ']', ')', '>')
def one_type(a, b):
	return a == '{' and b == '}' or a == '[' and b == ']' or a == '<' and b == '>' or a == '(' and b == ')'

s = raw_input()
st = []
q = 0
for i in s:
	if is_left(i):
		st.append(i)
	if is_right(i):
		if len(st) == 0:
			st.append(1)
			break
		cur = st.pop()
		if not one_type(cur, i):
			q += 1
print q if len(st) == 0 else 'Impossible'