You are given string *s* consists of opening and closing brackets of four kinds &lt;&gt;, {}, [], (). 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 &lt; by the bracket {, but you can't replace it by ) or &gt;.

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 *s*<sub class="lower-index">1</sub> and *s*<sub class="lower-index">2</sub> be a RBS then the strings &lt;*s*<sub class="lower-index">1</sub>&gt;*s*<sub class="lower-index">2</sub>, {*s*<sub class="lower-index">1</sub>}*s*<sub class="lower-index">2</sub>, [*s*<sub class="lower-index">1</sub>]*s*<sub class="lower-index">2</sub>, (*s*<sub class="lower-index">1</sub>)*s*<sub class="lower-index">2</sub> are also RBS.

For example the string "[[(){}]&lt;&gt;]" is RBS, but the strings "[)()" and "][()()" are not.

Determine the least number of replaces to make the string *s* RBS.
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 10<sup class="upper-index">6</sup>.
none
[<}){}
2
{()}[]
0
]]
Impossible
>
Impossible
{}
0
{}
0
{]
1
{]
1
{]
1
[]{[]({)([
Impossible
(([{>}{[{[)]]>>]
7
((<>)[]<]><]
3
[[([[(>]>)))[<)>
6
({)[}<)](}
5
(}{)[<][)(]}
6
>}({>]{[}<{<{{)[]]{)]>]]]<(][{)<<<{<<)>)()[>{<]]{}<>}}}}(>}<})(][>{((<{<)]}>)))][>[}[])<]){]]][<[)([
Impossible
<<[<{{<([({<<[)<>(]]){})>[](])[)))[[}>]<)>[[>{>>>[<]}<>>)[>]<{)<[><(<]][>(>]>][(<][{]}(()<[()[>><<])<]})]<]}{)
45
[<<{{((}[}<<)<)>})(][{>}})((>)<[)[>}[})[)>()[()[((}<<(>)<>](<>(}[>})[[[{)<}<<(}{>>}[<([[])<><)]<{>}[>>>{({>)}]})>)
42
(<[([(<({>(}{]>[(})])}])()<<}{]{[>]>(>>[(>>}[){(}<[{(()]{{<(<{][[{<><{<{)<>>]}}}{)(}{})}[<))>>}((({>){({}{{]}]>>}})>))
43
{(]}<([]<]{>]<{<({{{<>))}[({(}{)[}({>]}}<<)}<]))(<>(>{>{{{)<}({<]<>{)(>[)>{({}<([<[[)]><>{]}}(>]{}<)[})]}]]}]}>}
40
<(([)]<[}>{)>][[(<()({{{>>((]<}<{{<>}><<[)}[[)([[)[)}<]<{(<>){([)><{[([[][({])})<][(}]}>>[){)[({>){(}[}})>}>]>)]}))})>}]
45
)(
Impossible
[[[[[[[[
Impossible
import re
from copy import deepcopy
myin = input()
# myin = '[<}){}'
# myin = '{()}[]'
# myin = ']]'

LIMIT = 3000

def cleanup(cleanup_src):
    mypattern = r'(\{\}|\(\)|\[\]|\<\>)'
    if not re.search(mypattern, cleanup_src):
        return cleanup_src, -1
    limiter = 0
    changed = True
    while changed and limiter < LIMIT:
        limiter += 1
        changed = False
        if re.search(mypattern, cleanup_src):
            changed = True
            cleanup_src = re.sub(mypattern, '', cleanup_src)
    return cleanup_src, 0

def exchange(src):
    counter = 0
    limiter = 0
    changed = True
    src, errcode = cleanup(src)
    mypattern = r'(\{|\(|\[|\<)(\}|\)|\]|\>)'
    while changed and limiter < LIMIT:
        if len(src) > 0 and src[0] in ('}', ')', ']', '>'):
            return -1, src
        if len(src) > 0 and src[-1] in ('{', '(', '[', '<'):
            return -1, src
        changed = False
        limiter += 1
        if re.search(mypattern, src):
            # print(src, counter)
            changed = True
            src = re.sub(mypattern, '', src, 1)
            counter += 1
            src, errcode = cleanup(src)
    return counter, src

counter, myout = exchange(myin)
# print(myout)
print("Impossible" if myout != "" else counter)