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 isEqual(char a, char b) {
  if (a == '(' && b == ')')
    return true;
  else if (a == '<' && b == '>')
    return true;
  else if (a == '[' && b == ']')
    return true;
  else if (a == '{' && b == '}')
    return true;
  return false;
}
int main(void) {
  string str;
  stack<char> stck, stck2;
  getline(cin, str);
  if (str == "\n")
    return 0 * puts(0);
  else if (str.size() % 2 != 0)
    return 0 * puts("Impossible");
  int cnt = 0;
  for (int i = 0; i < str.size(); i++) {
    if (str[i] == '<' || str[i] == '{' || str[i] == '[' || str[i] == '(') {
      stck.push(str[i]);
    } else {
      if (stck.empty()) return 0 * puts("Impossible");
      if (!isEqual(stck.top(), str[i])) cnt++;
      stck.pop();
    }
  }
  int cnt2 = 0;
  for (int i = str.size() - 1; i >= 0; i--) {
    if (str[i] == '>' || str[i] == '}' || str[i] == ']' || str[i] == ')') {
      stck2.push(str[i]);
    } else {
      if (stck2.empty() && cnt == 0) return 0 * puts("Impossible");
      if (!stck2.empty()) {
        if (!isEqual(stck2.top(), str[i])) cnt2++;
        stck2.pop();
      }
    }
  }
  if (!stck.empty() || !stck2.empty())
    cout << "Impossible" << endl;
  else
    cout << min(cnt, cnt2) << endl;
  return 0;
}