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 JAVA):

Solution:

import java.util.*;
import java.io.*;

public class CodeForces {

    static int dx[] = {1, 0, -1, 0, 1, 1, -1, -1};
    static int dy[] = {0, 1, 0, -1, 1, -1, 1, -1};
    static final int INF = (int) 1e9 + 10;

    static char inv(char ch){
        if(ch == '{')
            return '}';
        else if(ch == '(')
            return ')';
        else if(ch == '<')
            return '>';
        return ']';
    }
    public static void main(String[] args) throws IOException {
        in.init(System.in);
        String s = in.n();
        Stack<Character> stack = new Stack();
        int ans = 0;
        
        for (int i = 0; i < s.length(); i++) {
            char ch = s.charAt(i);
            
            if(ch == '}' || ch == '>' || ch == ')' || ch == ']'){
                if(!stack.isEmpty()){
                    if(inv(stack.pop()) != ch){
                        ans++;
                    }
                }
                else{
                    System.out.println("Impossible");
                    return;
                }
            }
            
            else
                stack.push(ch);
        }
        
        if(stack.isEmpty())
            System.out.println(ans);
        else
            System.out.println("Impossible");
    }
}
class Queue {

    int first = -1, last = -1, size = 0;
    long arr[];

    Queue(int n) {
        arr = new long[n + 10];
    }

    long pop() {
        size--;
        return arr[++first];
    }

        void push(long x) {
        size++;
        arr[++last] = x;
    }

    boolean isEmpty() {
        return first == last;
    }
}

class Pair implements Comparable<Pair> {

    int x;
    int y;

    Pair(int a, int b) {
        x = a;
        y = b;
    }

    @Override
    public int compareTo(Pair t) {
        return x - t.x;
    }

    @Override
    public int hashCode() {
        return 1;
    }

    @Override
    public boolean equals(Object o) {
        return ((Pair) o).x == x && ((Pair) o).y == y;
    }

}

class in {

    static BufferedReader reader;
    static StringTokenizer tokenizer;

    public static int pars(String x) {
        int num = 0;
        int i = 0;
        if (x.charAt(0) == '-') {
            i = 1;
        }
        for (; i < x.length(); i++) {
            num = num * 10 + (x.charAt(i) - '0');
        }

        if (x.charAt(0) == '-') {
            return -num;
        }

        return num;
    }

    static void init(InputStream input) {
        reader = new BufferedReader(
                new InputStreamReader(input));
        tokenizer = new StringTokenizer("");
    }

    static void init(FileReader input) {
        reader = new BufferedReader(input);
        tokenizer = new StringTokenizer("");
    }

    static String n() throws IOException {
        while (!tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(
                    reader.readLine());
        }
        return tokenizer.nextToken();
    }

    static int i() throws IOException {
        return pars(n());
    }

    static long l() throws IOException {
        return Long.parseLong(n());
    }

    static double d() throws IOException {
        return Double.parseDouble(n());
    }
}