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:
s = list(input())
x = list("<>{}[]()")
l = [0] * 4
d = {}
k = 0
o, c = 0, 0
f = 1
ans = 0
for t in s:
    y = x.index(t)
    yy = y // 2
    if y % 2 == 0:
        if f:
            k += 1
        o += 1
        d[k] = yy
        f = 1
    else:
        if not f:
            k -= 1
        if k <= 0:
            print("Impossible")
            exit()
        c += 1
        f = 0
        if not d[k] == yy:
            ans += 1
print(ans if o == c else "Impossible")