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 com(char c1, char c2) {
  if (c1 == '(' && c2 == ')' || c1 == '[' && c2 == ']' ||
      c1 == '{' && c2 == '}' || c1 == '<' && c2 == '>')
    return 0;
  else if ((c1 == '<' || c1 == '[' || c1 == '{' || c1 == '(') &&
           (c2 == '>' || c2 == ']' || c2 == '}' || c2 == ')'))
    return 1;
  else
    return 2;
}
stack<char> sta;
string s;
int main() {
  cin >> s;
  int change = 0;
  int is = true;
  for (int i = 0; i < s.length(); i++) {
    if (s[i] == '(' || s[i] == '[' || s[i] == '<' || s[i] == '{')
      sta.push(s[i]);
    else {
      if (sta.empty()) {
        is = false;
        break;
      } else if (com(sta.top(), s[i]) == 0) {
        sta.pop();
      } else if (com(sta.top(), s[i]) == 1) {
        change++;
        sta.pop();
      } else {
        is = false;
        break;
      }
    }
  }
  if (!sta.empty()) is = false;
  if (!is)
    cout << "Impossible";
  else
    cout << change;
  return 0;
}