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;
char arr[1000010];
char st[1000010];
int main() {
  int i, j, n, k, temp = 0;
  cin >> arr;
  k = strlen(arr);
  bool f = true;
  for (i = 0; i < k; i++) {
    if (arr[i] == '<' || arr[i] == '(' || arr[i] == '[' || arr[i] == '{')
      temp++;
    else
      temp--;
    if (temp < 0) {
      f = false;
      break;
    }
  }
  int answer = 0;
  if (f && temp == 0) {
    j = 0;
    for (i = 0; i < k; i++) st[i] = 'f';
    for (i = 0; i < k; i++) {
      if (arr[i] == '<' || arr[i] == '(' || arr[i] == '[' || arr[i] == '{')
        st[j++] = arr[i];
      else {
        if (!((arr[i] == ')' && st[j - 1] == '(') ||
              (arr[i] == '>' && st[j - 1] == '<') ||
              (arr[i] == '}' && st[j - 1] == '{') ||
              (arr[i] == ']' && st[j - 1] == '['))) {
          answer++;
        }
        st[--j] = 'f';
      }
    }
    cout << answer;
  } else
    cout << "Impossible";
  return 0;
}