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;
stack<char> st;
int main() {
  string s;
  cin >> s;
  int cnt = 0, m = 0;
  int n = s.length();
  for (int i = 0; i < n; i++) {
    if (s[0] == ']' || s[0] == '}' || s[0] == ')' || s[0] == '>') {
      cout << "Impossible" << endl;
      m++;
      break;
    } else {
      if (st.size() == 0) {
        st.emplace(s[i]);
      } else {
        if (s[i] == ']') {
          if (st.top() == '[') {
            st.pop();
          } else if (st.top() == '{' || st.top() == '<' || st.top() == '(') {
            st.pop();
            cnt++;
          }
        } else if (s[i] == '}') {
          if (st.top() == '{') {
            st.pop();
          } else if (st.top() == '[' || st.top() == '<' || st.top() == '(') {
            st.pop();
            cnt++;
          }
        } else if (s[i] == '>') {
          if (st.top() == '<') {
            st.pop();
          } else if (st.top() == '[' || st.top() == '{' || st.top() == '(') {
            st.pop();
            cnt++;
          }
        } else if (s[i] == ')') {
          if (st.top() == '(') {
            st.pop();
          } else if (st.top() == '[' || st.top() == '<' || st.top() == '{') {
            st.pop();
            cnt++;
          }
        } else {
          st.emplace(s[i]);
        }
      }
    }
  }
  if (st.size() > 0)
    cout << "Impossible\n";
  else if (m != 1)
    cout << cnt << endl;
  return 0;
}