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 PYTHON):

Solution:
from sys import stdin

s = stdin.readline().strip()

open_p = "<{[("
close_p = ">}])"

p = {}
for op, cl in zip(open_p, close_p):
    p[op] = cl

repl = 0
stack = []


def main(stack, repl, p):
    for char in s:
        if char in open_p:
            stack.append(char)
        if char in close_p:
            if len(stack) == 0:
                print "Impossible"
                return
            if p[stack.pop()] != char:
                repl += 1
    if len(stack) == 0:
        print repl
    else:
        print "Impossible"



main(stack, repl, p)