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() {
  stack<char> e;
  string c;
  cin >> c;
  int f = 0;
  for (int i = 0; i < c.size(); i++) {
    if (c[i] == '(' || c[i] == '<' || c[i] == '{' || c[i] == '[') e.push('(');
    if ((c[i] == ')' || c[i] == '>' || c[i] == '}' || c[i] == ']') &&
        e.size() != 0) {
      e.pop();
      f++;
    }
  }
  if (f * 2 != c.size())
    cout << "Impossible" << endl;
  else {
    f = 0;
    for (int i = 0; i < c.size(); i++) {
      if (c[i] == '(' || c[i] == '<' || c[i] == '{' || c[i] == '[')
        e.push(c[i]);
      if (c[i] == ')' || c[i] == '>' || c[i] == '}' || c[i] == ']') {
        if (c[i] == ')' && e.top() != '(')
          f++;
        else if (c[i] == '>' && e.top() != '<')
          f++;
        else if (c[i] == ']' && e.top() != '[')
          f++;
        else if (c[i] == '}' && e.top() != '{')
          f++;
        e.pop();
      }
    }
    cout << f << endl;
  }
  return 0;
}