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;
const long long MOD = 1E9 + 7;
bool open(char ch) { return ch == '(' || ch == '<' || ch == '[' || ch == '{'; }
bool match(char ch1, char ch2) {
  return ((ch1 == '{' && ch2 == '}') || (ch1 == '[' && ch2 == ']') ||
          (ch1 == '<' && ch2 == '>') || (ch1 == '(' && ch2 == ')'));
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  if (fopen("inp.txt", "r")) {
    freopen("inp.txt", "r", stdin);
    freopen("outp.txt", "w", stdout);
  }
  string s;
  cin >> s;
  long long ans = 0, i;
  stack<char> st;
  bool poss = true;
  for (i = 0; i < s.length(); i++) {
    if (open(s[i]))
      st.push(s[i]);
    else {
      if (st.empty() || !open(st.top())) {
        poss = false;
        break;
      }
      if (!match(st.top(), s[i])) {
        ans++;
      }
      st.pop();
    }
  }
  if (!st.empty()) poss = false;
  if (poss)
    cout << ans;
  else
    cout << "Impossible";
  return 0;
}