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;
vector<int> v;
bool sol(int i, int s, int n) {
  if (i == n) {
    if (s % 360 == 0)
      return 1;
    else
      return 0;
  }
  return sol(i + 1, s + v[i], n) || sol(i + 1, s - v[i], n);
}
int main() {
  int c = 0;
  string s;
  cin >> s;
  int n = s.size();
  stack<char> s1;
  s1.push(s[0]);
  for (int i = 1; i < n; i++) {
    if ((s[i] == ')' || s[i] == '}' || s[i] == '>' || s[i] == ']') &&
        s1.size() > 0) {
      if (s[i] == ')') {
        if (s1.top() == '(')
          s1.pop();
        else if (s1.top() == '{' || s1.top() == '<' || s1.top() == '[') {
          s1.pop();
          c++;
        }
      } else {
        if (s[i] == '}') {
          if (s1.top() == '{')
            s1.pop();
          else if (s1.top() == '(' || s1.top() == '<' || s1.top() == '[') {
            s1.pop();
            c++;
          }
        } else {
          if (s[i] == ']') {
            if (s1.top() == '[')
              s1.pop();
            else if (s1.top() == '{' || s1.top() == '<' || s1.top() == '(') {
              s1.pop();
              c++;
            }
          } else {
            if (s[i] == '>') {
              if (s1.top() == '<')
                s1.pop();
              else if (s1.top() == '{' || s1.top() == '(' || s1.top() == '[') {
                s1.pop();
                c++;
              }
            }
          }
        }
      }
    } else
      s1.push(s[i]);
  }
  if (s1.size() == 0)
    cout << c << endl;
  else
    cout << "Impossible\n";
  return 0;
}