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:
def solve():
    S = input()

    P = {
        '>': '<',
        ']': '[',
        ')': '(',
        '}': '{',
    }

    stack = []
    n = 0
    ans = 0
    for i, c in enumerate(S):
        if c in '<[{(':
            n += 1
            stack.append(c)
        else:
            n -= 1
            if len(stack) == 0:
                print('Impossible')
                return
            x = stack.pop()
            if x != P[c]:
                ans += 1

    if n != 0:
        print('Impossible')
        return

    print(ans)


if __name__ == '__main__':
    solve()