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
from functools import wraps
import time


myin = input()
# myin = '[<}){}'
# myin = '{()}[]'
# myin = ']]'
# myin = '<(([)]<[}>{)>][[(<()({{{>>((]<}<{{<>}><<[)}[[)([[)[)}<]<{(<>){([)><{[([[][({])})<][(}]}>>[){)[({>){(}[}})>}>]>)]}))})>}]'
# 45
DEBUG = 0


def timeit(func):
    @wraps(func)
    def timeit_wrapper(*args, **kwargs):
        start_time = time.perf_counter()
        result = func(*args, **kwargs)
        end_time = time.perf_counter()
        total_time = end_time - start_time
        if DEBUG:
          print(f'Function {func.__name__}{args} {kwargs} Took {total_time:.4f} seconds')
        return result
    return timeit_wrapper

@timeit
def cleanup(cleanup_src):
  mypattern = r'(\{\}|\(\)|\[\]|\<\>)'
  if not re.search(mypattern, cleanup_src):
    return cleanup_src
  changed = True
  while changed:
    changed = False
    if re.search(mypattern, cleanup_src):
      changed = True
      cleanup_src = re.sub(mypattern, '', cleanup_src)
  return cleanup_src

def exchange(src):
  counter = 0
  changed = True
  debug(src)
  src = cleanup(src)
  debug(src)
  mypattern = r'(\{|\(|\[|\<)(\}|\)|\]|\>)'
  while changed :
    if len(src) > 0 \
      and \
        (src[0] in ('}', ')', ']', '>') \
        or src[-1] in ('{', '(', '[', '<')):
          return -1, src
    changed = False
    debug("SRC: ")
    debug(src)
    debug("FINDALL: ")
    debug(re.findall(mypattern, src))
    if DEBUG:
      for i in re.finditer(mypattern, src):
        debug(i)
    debug(len(re.findall(mypattern, src)))
    if (found := len(re.findall(mypattern, src))) > 0:
      # debug(src, counter)
      changed = True
      src = re.sub(mypattern, '', src)
      counter += found
      debug("COUNTER: ")
      debug(counter)
      src = cleanup(src)
  return counter, src

def debug(s: str):
  if DEBUG:
    print(s)


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