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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
stack<char> a;
int main() {
  ios_base::sync_with_stdio(0);
  string s;
  cin >> s;
  int k = 0;
  bool f = 0;
  for (int i = 0; i < s.size(); i++) {
    if (s[i] == '<' or s[i] == '(' or s[i] == '{' or s[i] == '[')
      a.push(s[i]);
    else {
      char q;
      if (a.empty()) {
        f = 1;
        break;
      }
      q = a.top();
      a.pop();
      if (s[i] == '>' and q != '<')
        k++;
      else if (s[i] == ')' and q != '(')
        k++;
      else if (s[i] == '}' and q != '{')
        k++;
      else if (s[i] == ']' and q != '[')
        k++;
    }
  }
  if (f == 1 or !a.empty())
    cout << "Impossible";
  else
    cout << k;
  return 0;
}