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> mystack;
  string s;
  cin >> s;
  int i, count = 0;
  for (i = 0; i < s.length(); i++) {
    if (mystack.empty() &&
        (s[i] == '}' || s[i] == ']' || s[i] == '>' || s[i] == ')')) {
      cout << "Impossible" << endl;
      return 0;
    } else if (s[i] == '{' || s[i] == '[' || s[i] == '<' || s[i] == '(') {
      mystack.push(s[i]);
      continue;
    } else {
      if ((mystack.top() == '[' && s[i] == ']') ||
          (mystack.top() == '<' && s[i] == '>') ||
          (mystack.top() == '{' && s[i] == '}') ||
          (mystack.top() == '(' && s[i] == ')')) {
        mystack.pop();
        continue;
      } else {
        count++;
        mystack.pop();
      }
    }
  }
  if (!mystack.empty())
    cout << " Impossible " << endl;
  else
    cout << count << endl;
  return 0;
}