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:
import sys

INF = 10 ** 18 + 3


def main():
    opening = "<{[("
    closing = ">}])"
    s = input()
    stack = []
    res = 0
    for i, sym in enumerate(s):
        if sym in opening:
            kind = opening.find(sym)
            stack.append(kind)
        else:
            kind = closing.find(sym)
            if not stack:
                res = -1
                break
            if stack[-1] != kind:
                res += 1
            del stack[-1]

    print("Impossible" if res == -1 or stack else res)


def set_input(file):
    global input
    input = lambda: file.readline().rstrip()


def set_output(file):
    global print
    lprint = print

    def print(*args, **kwargs):
        kwargs["file"] = kwargs.get("file", file)
        return lprint(*args, **kwargs)


if __name__ == '__main__':
    is_mine = "MINE" in sys.argv
    set_input(open("input.txt", "r") if is_mine else sys.stdin)
    set_output(sys.stdout if is_mine else sys.stdout)
    main()