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 a[1000011];
int main() {
  while (~scanf("%s", a)) {
    int t = strlen(a);
    if (t % 2 != 0)
      printf("Impossible\n");
    else {
      stack<char> sta;
      int ans = 0, p = 0;
      for (int i = 0; i < t; i++) {
        if (a[i] == '{' || a[i] == '[' || a[i] == '(' || a[i] == '<') {
          sta.push(a[i]);
          ans++;
        } else {
          if (sta.empty()) {
            p++;
            printf("Impossible\n");
            break;
          } else {
            char s = sta.top();
            if ((s == '{' && a[i] == '}') || (s == '(' && a[i] == ')') ||
                (s == '[' && a[i] == ']') || (s == '<' && a[i] == '>')) {
              ans--;
            }
            sta.pop();
          }
        }
      }
      if (p == 0) {
        if (sta.empty()) {
          if (ans < 0)
            printf("Impossible\n");
          else
            printf("%d\n", ans);
        } else
          printf("Impossible\n");
      }
    }
    memset(a, 0, sizeof(a));
  }
  return 0;
}