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.*;
import java.util.stream.*;

public class Edu4C {
    private static boolean debug = false;

    private static String str;
    private static int[] A;

    private static void solveProblem(InputStream instr) throws Exception {
        InputReader sc = new InputReader(instr);
        int testCount = 1;
        if (debug) {
            testCount = sc.nextInt();
        }

        for (int t = 1; t <= testCount; t++) {
            printDebug("------ " + t + " ------");
            str = sc.next();
            Object result = solveTestCase();
            System.out.println(result);
        }
    }

    private static Object solveTestCase() {
        char[] A = str.toCharArray();
        int leftCount = 0;
        int rightCount = 0;
        int ans = 0;
        Stack<Integer> set = new Stack<>();
        Deque<Character> stack = new ArrayDeque<>();
        for(int i = 0; i < A.length; i++) {
            char ch = A[i];
            if (ch == '[' || ch == '<' || ch == '{' || ch == '(') {
                leftCount++;
                stack.addLast(ch);
            } else {
                rightCount++;
                if (rightCount > leftCount) {
                 //   System.out.println("Return");
                    return "Impossible";
                }
                char last = stack.pollLast();
                if (last == '[' && ch != ']') {
                    ans++;
                }
                if (last == '{' && ch != '}') {
                    ans++;
                }
                if (last == '(' && ch != ')') {
                    ans++;
                }
                if (last == '<' && ch != '>') {
                    ans++;
                }
            }
        }
       // System.out.println(leftCount + " " + rightCount);
        if(rightCount != leftCount){
            return "Impossible";
        }

        return ans;
    }

    private static int[] readInts(InputReader sc, int N) throws Exception {
        int[] arr = new int[N];
        for (int i = 0; i < N; i++) {
            arr[i] = sc.nextInt();
        }
        return arr;
    }

    private static String joinValues(List<? extends Object> list, String delim) {
        return list.stream().map(Object::toString).collect(Collectors.joining(delim));
    }

    private static String joinValues(int[] arr, String delim) {
        List<Object> list = new ArrayList<>();
        for (Object value : arr) {
            list.add(value);
        }
        return list.stream().map(Object::toString).collect(Collectors.joining(delim));
    }

    private static class Pair {
        int x, y;
        Pair(int x, int y){
            this.x = x;
            this.y = y;
        }
    }

    public static void printDebug(Object str) {
        if (debug) {
            System.out.println("DEBUG: " + str);
        }
    }


    private static void printOut(String out) {
        System.out.println(out);
    }

    public static String printArr(int[] arr) {
        StringBuilder builder = new StringBuilder();
        for (int in : arr) {
            builder.append(in).append(" ");
        }
        return builder.toString();
    }

    public static void shuffle(int[] array) {
        Random rand = new Random();
        for (int i = 0; i < array.length; i++) {
            int x = rand.nextInt(array.length - i);
            int idx = x + i;
            int tmp = array[idx];
            array[idx] = array[i];
            array[i] = tmp;
        }
    }
    private static final class InputReader {
        private final InputStream stream;
        private final byte[] buf = new byte[1024];
        private int curChar;
        private int Chars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        private int read() throws Exception {
            if (curChar >= Chars) {
                curChar = 0;
                Chars = stream.read(buf);
                if (Chars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public final int nextInt() throws Exception {
            return (int)nextLong();
        }

        public final long nextLong() throws Exception {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
                if (c == -1)
                    throw new IOException();
            }
            boolean negative = false;
            if (c == '-') {
                negative = true;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += (c - '0');
                c = read();
            } while (!isSpaceChar(c));
            return negative ? (-res) : (res);
        }

        public final int[] nextIntBrray(int size) throws Exception {
            int[] arr = new int[size];
            for (int i = 0; i < size; i++)
                arr[i] = nextInt();
            return arr;
        }

        public final String next() throws Exception {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.append((char)c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public final String nextLine() throws Exception {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.append((char)c);
                c = read();
            } while (c != '\n' && c != -1);
            return res.toString();
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
    }

    public static void main(String[] args) throws Exception {
        long currTime = System.currentTimeMillis();
        try {
            if (new File("input.in").exists()) {
                debug = true;
            }
        } catch (Throwable ex) {

        }
        if (debug) {
            solveProblem(new FileInputStream(new File("input.in")));
            System.out.println("Time: " + (System.currentTimeMillis() - currTime));
        } else {
            solveProblem(System.in);
        }
    }

}