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;
char ch[1000006];
int main() {
  int o = 0, c = 0;
  scanf("%s", ch);
  int len = strlen(ch);
  for (int i = 0; i < len; i++) {
    if (ch[i] == '[' || ch[i] == '<' || ch[i] == '(' || ch[i] == '{') {
      o++;
    } else {
      c++;
    }
  }
  if (o != c) {
    cout << "Impossible";
    return 0;
  }
  stack<char> s;
  int ans = 0;
  int flag = 1;
  for (int i = 0; i < len; i++) {
    if (i == 0) {
      if (ch[i] == '[' || ch[i] == '<' || ch[i] == '(' || ch[i] == '{') {
        s.push(ch[i]);
      } else {
        s.push(ch[i]);
        flag = 0;
      }
    } else {
      if (ch[i] == '[' || ch[i] == '<' || ch[i] == '(' || ch[i] == '{') {
        s.push(ch[i]);
      } else {
        if (s.empty()) {
          flag = 0;
          break;
        }
        char temp = s.top();
        s.pop();
        if (ch[i] == ')') {
          if (temp == '(')
            ;
          else
            ans++;
        } else if (ch[i] == '}') {
          if (temp == '{')
            ;
          else
            ans++;
        } else if (ch[i] == ']') {
          if (temp == '[')
            ;
          else
            ans++;
        } else if (ch[i] == '>') {
          if (temp == '<')
            ;
          else
            ans++;
        }
      }
    }
    if (flag == 0) {
      break;
    }
  }
  if (flag == 0) {
    cout << "Impossible";
    return 0;
  }
  cout << ans;
  return 0;
}