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;
bool isOpen(char c) { return c == '[' || c == '{' || c == '(' || c == '<'; }
bool isClose(char c) { return c == ']' || c == '}' || c == ')' || c == '>'; }
bool areSameType(char c1, char c2) {
  return (c1 == '[' && c2 == ']') || (c1 == '{' && c2 == '}') ||
         (c1 == '(' && c2 == ')' || (c1 == '<' && c2 == '>'));
}
int main() {
  char c;
  string s;
  int i, ans = 0;
  bool valid = true;
  stack<char> myStack;
  cin >> s;
  for (i = 0; i < s.length(); i++) {
    c = s[i];
    if (isOpen(s[i])) {
      myStack.push(c);
    } else if (isClose(s[i])) {
      if (myStack.size() > 0) {
        if (!areSameType(myStack.top(), s[i])) {
          ans++;
        }
        myStack.pop();
      } else {
        valid = false;
      }
    }
  }
  if (myStack.size() == 0 && valid) {
    cout << ans << endl;
  } else {
    cout << "Impossible\n";
  }
  return 0;
}