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 sys import stdin


def main():
    s = stdin.readline()
    stack = []
    ok = True
    ans = 0
    close = '>}])'
    open = '<{[('
    for i in range(len(s) - 1):
        if s[i] in close:
            if not stack:
                ok = False
                break
            else:
                i1 = close.index(s[i])
                i2 = open.index(stack[-1])
                if i1 != i2:
                    ans += 1
                stack.pop()
        else:
            stack.append(s[i])
    if stack or not ok:
        print('Impossible')
    else:
        print(ans)


if __name__ == '__main__':
    main()