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;
int main() {
  int cn = 0;
  string s;
  cin >> s;
  vector<char> v;
  for (int i = 0; i < s.size(); i++) {
    if (s[i] == '(') v.push_back('(');
    if (s[i] == '{') v.push_back('{');
    if (s[i] == '<') v.push_back('<');
    if (s[i] == '[') v.push_back('[');
    if (s[i] == ')') {
      if (v.empty()) {
        v.push_back('1');
        break;
      }
      if (v.back() != '(') cn++;
      v.pop_back();
    }
    if (s[i] == '}') {
      if (v.empty()) {
        v.push_back('1');
        break;
      }
      if (v.back() != '{') cn++;
      v.pop_back();
    }
    if (s[i] == '>') {
      if (v.empty()) {
        v.push_back('1');
        break;
      }
      if (v.back() != '<') cn++;
      v.pop_back();
    }
    if (s[i] == ']') {
      if (v.empty()) {
        v.push_back('1');
        break;
      }
      if (v.back() != '[') cn++;
      v.pop_back();
    }
  }
  if (v.empty())
    cout << cn;
  else
    puts("Impossible");
}