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() {
  string s;
  cin >> s;
  int n = s.length();
  string r(s);
  for (int i = 0; i < n; i++) {
    if (r[i] == '<' || r[i] == '[' || r[i] == '(' || r[i] == '{') {
      r[i] = '(';
    } else {
      r[i] = ')';
    }
  }
  stack<char> s1;
  bool flag = true;
  for (int i = 0; i < r.length(); i++) {
    if (s1.size() > 0) {
      if (r[i] == ')') {
        if (s1.top() == '(') {
          s1.pop();
        } else {
          flag = false;
        }
      } else {
        s1.push(r[i]);
      }
    } else {
      if (r[i] == ')')
        flag = false;
      else
        s1.push(r[i]);
    }
  }
  if (s1.size() > 0) flag = false;
  if (flag) {
    int ctr = 0;
    stack<char> s2;
    for (int i = 0; i < s.length(); i++) {
      if (s2.size() == 0) {
        s2.push(s[i]);
      } else {
        if (s2.top() == '(') {
          if (s[i] == ')') {
            s2.pop();
          } else if (s[i] == '}' || s[i] == '>' || s[i] == ']') {
            ctr++;
            s2.pop();
          } else {
            s2.push(s[i]);
          }
        } else if (s2.top() == '{') {
          if (s[i] == '}') {
            s2.pop();
          } else if (s[i] == ')' || s[i] == '>' || s[i] == ']') {
            ctr++;
            s2.pop();
          } else {
            s2.push(s[i]);
          }
        } else if (s2.top() == '[') {
          if (s[i] == ']') {
            s2.pop();
          } else if (s[i] == '}' || s[i] == '>' || s[i] == ')') {
            ctr++;
            s2.pop();
          } else {
            s2.push(s[i]);
          }
        } else if (s2.top() == '<') {
          if (s[i] == '>') {
            s2.pop();
          } else if (s[i] == '}' || s[i] == ')' || s[i] == ']') {
            ctr++;
            s2.pop();
          } else {
            s2.push(s[i]);
          }
        }
      }
    }
    cout << ctr;
  } else {
    cout << "Impossible";
  }
}