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 collections
moji =  '{()}[]'
c = collections.Counter(moji)

ans = 0
if c['{'] + c['<'] + c['('] +c['['] != c['}'] + c['>'] + c[')'] +c[']']:
 print('Impossible')
else:
  i = 0
  l = 0
  l_1 = 0
  l_2 = 0
  l_3 = 0
  l_4 = 0
  r = 0
  r_1 = 0
  r_2 = 0
  r_3 = 0
  r_4 = 0
  while i < len(moji):
    if moji[i] in set(['[']):
      r += 1
      r_1 += 1
    elif moji[i] in set(['(']):
      r += 1
      r_2 += 1
    elif moji[i] in set(['<']):
      r += 1
      r_3 += 1
    elif moji[i] in set(['{']):
      r += 1
      r_4 += 1
    elif moji[i] in set([']']):
      l += 1
      l_1 += 1
    elif moji[i] in set([')']):
      l += 1
      l_2 += 1
    elif moji[i] in set(['>']):
      l += 1
      l_3 += 1
    elif moji[i] in set(['}']):
      l += 1
      l_4 += 1
    if r < l:
      print('Impossible')
      break
    if r_1 == l_1 and r_1 != 0 and l_1 != 0:
      r_1 -= 1
      l_1 -= 1
    elif r_2 == l_2 and r_2 != 0 and l_2 != 0:
      r_2 -= 1
      l_2 -= 1
    elif r_3 == l_3 and r_3 != 0 and l_3 != 0:
      r_3 -= 1
      l_3 -= 1
    elif r_4 == l_4 and r_4 != 0 and l_4 != 0:
      r_4 -= 1
      l_4 -= 1
    if r > 0 and  l > 0:
      l -= 1
      r -= 1
      i += 1
    else:
      i += 1
      continue

if i == len(moji):
  print(r_1+r_2+r_3+r_4)