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;
string str;
stack<char> st;
int main() {
  int n, ans = 0, flag = 1;
  char ch;
  cin >> str;
  n = str.length();
  for (int i = 0; i < n; i++) {
    if (str[i] == '<' || str[i] == '{' || str[i] == '[' || str[i] == '(')
      st.push(str[i]);
    else if (!st.empty()) {
      ch = st.top();
      st.pop();
      if (str[i] == '>' && ch != '<')
        ans++;
      else if (str[i] == ')' && ch != '(')
        ans++;
      else if (str[i] == ']' && ch != '[')
        ans++;
      else if (str[i] == '}' && ch != '{')
        ans++;
    } else {
      flag = 0;
      break;
    }
  }
  if (flag && st.empty())
    printf("%d", ans);
  else
    printf("Impossible");
  return 0;
}