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;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  string s;
  cin >> s;
  long long n = s.size();
  stack<char> s1;
  long long open = 0, close = 0, ans = 0;
  for (long long i = 0; i < n; i++) {
    if (s[i] == ')' || s[i] == ']' || s[i] == '}' || s[i] == '>') {
      close++;
    } else {
      open++;
      s1.push(s[i]);
    }
    if (close > open) {
      cout << "Impossible\n";
      return 0;
    }
    if (s[i] == ')' || s[i] == ']' || s[i] == '}' || s[i] == '>') {
      if (s[i] == ')' && s1.top() != '(')
        ans++;
      else if (s[i] == '}' && s1.top() != '{')
        ans++;
      else if (s[i] == ']' && s1.top() != '[')
        ans++;
      else if (s[i] == '>' && s1.top() != '<')
        ans++;
      s1.pop();
    }
  }
  if (open != close) {
    cout << "Impossible\n";
    return 0;
  }
  cout << ans << "\n";
  return 0;
}