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.io.*;
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.StringTokenizer;

public class SNSTemplate implements Runnable {

    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok = new StringTokenizer("");

    void init() throws FileNotFoundException {
        try {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        } catch (Throwable e) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        }
    }

    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            try {
                tok = new StringTokenizer(in.readLine());
            } catch (Exception e) {
                return null;
            }
        }
        return tok.nextToken();
    }

    int readInt() throws IOException {
        return Integer.parseInt(readString());
    }

    int[] readIntArray(int size) throws IOException {
        int[] res = new int[size];
        for (int i = 0; i < size; i++) {
            res[i] = readInt();
        }
        return res;
    }

    long readLong() throws IOException {
        return Long.parseLong(readString());
    }

    double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }

    public static void main(String[] args) {
        new Thread(null, new SNSTemplate(), "", 1l * 200 * 1024 * 1024).start();
    }

    long timeBegin, timeEnd;

    void time() {
        timeEnd = System.currentTimeMillis();
        System.err.println("Time = " + (timeEnd - timeBegin));
    }

    long memoryTotal, memoryFree;

    void memory() {
        memoryFree = Runtime.getRuntime().freeMemory();
        System.err.println("Memory = " + ((memoryTotal - memoryFree) >> 10)
                + " KB");
    }

    public void run() {
        try {
            timeBegin = System.currentTimeMillis();
            memoryTotal = Runtime.getRuntime().freeMemory();
            init();
            solve();
            out.close();
            if (System.getProperty("ONLINE_JUDGE") == null) {
                time();
                memory();
            }
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(-1);
        }
    }

    boolean isOpen(char x) {
        return "{<[(".contains("" + x);
    }
    boolean eq(char x, char y) {
        if (x == '{' && y == '}') return true;
        if (x == '<' && y == '>') return true;
        if (x == '[' && y == ']') return true;
        if (x == '(' && y == ')') return true;
        return false;
    }


    void solve() throws IOException {
        char[] x = readString().toCharArray();
        int balance = 0;
        for (int i = 0; i < x.length; i++) {
            if (isOpen(x[i])) balance++;
            else balance--;
            if (balance < 0) {
                out.println("Impossible");
                return;
            }
        }
        if (balance != 0) {
            out.println("Impossible");
            return;
        }
        int[] indexClose = new int[x.length];
        Arrays.fill(indexClose, -1);
        ArrayDeque<Integer> deq = new ArrayDeque<>();
        for (int i = 0; i < x.length; i++) {
            if (isOpen(x[i])) {
                deq.add(i);
            } else {
                indexClose[deq.pollLast()] = i;
            }
        }
        int ans = 0;
        for (int i=0;i<x.length;i++) {
            if (indexClose[i] == -1) continue;
            if (!eq(x[i], x[indexClose[i]])) ans++;
        }
        out.println(ans);

    }
}