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) {
  bool open = false;
  if (c == '<' || c == '{' || c == '[' || c == '(') {
    open = true;
  }
  return open;
}
bool ismatch(char a, char b) {
  bool match = false;
  if (a == '<' && b == '>') {
    match = true;
  }
  if (a == '{' && b == '}') {
    match = true;
  }
  if (a == '[' && b == ']') {
    match = true;
  }
  if (a == '(' && b == ')') {
    match = true;
  }
  return match;
}
int main() {
  long long replaces = 0;
  string s;
  cin >> s;
  stack<char> st;
  long long n = strlen(s.c_str());
  for (long long i = 0; i < n; i++) {
    if (isopen(s[i])) {
      if (i == n - 1) {
        cout << "Impossible" << endl;
        return 0;
      } else {
        st.push(s[i]);
      }
    } else {
      if (!st.empty()) {
        if (ismatch(st.top(), s[i])) {
          st.pop();
        } else {
          st.pop();
          replaces++;
        }
      } else {
        cout << "Impossible" << endl;
        return 0;
      }
    }
  }
  cout << replaces << endl;
}