Replace To Make Regular Bracket Sequence

Replace To Make Regular Bracket Sequence

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

[<}){}

Output

2

Input

{()}[]

Output

0

Input

]]

Output

Impossible

题意：输入一行括号序列，左边括号可以和右括号抵消。右括号可以转换为其他类型右括号进行成对抵消。输出需要转换的个数。如果无法抵消输出"Impossible"

#include <iostream>
#include <stack>
using namespace std;

int main(){
    string input;
    while(cin >> input){
        int count = 0;
        stack<char> s;
        s.push(input[0]); //[ 
        for(int i = 1;i < input.length();i++){//<}){}
            if(s.size() > 0 && (s.top() == '[' || s.top() == '<' || s.top() == '(' || s.top() == '{')){
                if(input[i] == ']' || input[i] == '>' || input[i] == ')' || input[i] == '}'){
                    if(!((s.top() == '[' && input[i] == ']') || 
                        (s.top() == '<' && input[i] == '>') || 
                        (s.top() == '(' && input[i] == ')') ||
                        (s.top() == '{' && input[i] == '}'))){
                        count++;
                    }
                    s.pop();
                }else{
                    s.push(input[i]);
                }
            }else{
                s.push(input[i]);
            }
        }
        if(s.size() != 0){
            cout << "Impossible" << endl;
        }else{
            cout << count << endl;
        }
    }
}