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:
from collections import deque
s = deque()
v = input()
ans = 0
for i in range(len(v)):
    if len(s) == 0:
        if (v[i] == ')') or (v[i] == '}') or (v[i] == ']') or (v[i] == '>'):
            print('Impossible')
            exit()
    if (v[i] == '(') or (v[i] == '<') or (v[i] == '[') or (v[i] == '{'):
        s.append(v[i])
    else:
        k = abs(ord(v[i]) - ord(s[len(s)-1]))
        if abs(ord(v[i]) - ord(s[len(s)-1])) <= 2:
            s.pop()
        else:
            ans += 1
            s.pop()
if len(s) != 0:
    print('Impossible')
else:
    print(ans)