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 Red {
    static FastScanner f;
    static PrintWriter pw = new PrintWriter(System.out);
    static long mod = 1000_000_007;
    static long oo = (long)3e18;
    static int ooo = (int)1e9;

    public static void solve()throws IOException {
        char s[] = f.next().toCharArray();
        Stack<Character> st = new Stack<>();
        int ans = 0;
        for (int i = 0; i < s.length; ++i) {
            char c = s[i];
            if (c == '(') st.push(c);
            else if (c == '{') st.push(c);
            else if (c == '<') st.push(c);
            else if (c == '[') st.push(c);
            else {
                if (st.size() == 0) {
                    pn("Impossible");
                    return;
                }
                char t = st.pop();
                if (c == ')' && t != '(') ++ans;
                if (c == ']' && t != '[') ++ans;
                if (c == '>' && t != '<') ++ans;
                if (c == '}' && t != '{') ++ans;
            }
        }

        if (st.size() != 0) pn("Impossible");
        else pn(ans);
    }   

    public static void main(String args[])throws IOException {
        go();
        boolean test_cases = false;
        int t = test_cases ? f.ni() : 1;
        while (t --> 0) solve();
        pw.flush();
        pw.close(); 
    }

    public static void go()throws IOException {
        if (System.getProperty("ONLINE_JUDGE") == null) {
            f = new FastScanner("");
        }
        else f = new FastScanner(System.in);
    }

    public static class FastScanner {
        StringTokenizer st;
        BufferedReader br;
 
        public FastScanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public FastScanner(String str) {
            try {
                br = new BufferedReader(new FileReader("inp.txt"));
            }
            catch (Exception e) {
                e.printStackTrace();
            }
        }
 
        public String next()throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }
 
        public int ni() throws IOException {return Integer.parseInt(next());}
 
        public long nl() throws IOException {return Long.parseLong(next());}
 
        public String nextLine() throws IOException {return br.readLine();}

        public double nd() throws IOException {return Double.parseDouble(next());}
    }

    public static long mul(long a , long b) {
        return ((a % mod) * (b % mod)) % mod;
    }

    public static void sort(int a[]) {
        ArrayList<Integer> x = new ArrayList<>();
        for (int i : a) x.add(i);
        Collections.sort(x);
        for (int i = 0; i < a.length; ++i) a[i] = x.get(i);
    }
    
    public static void sort(long a[]) {
        ArrayList<Long> x = new ArrayList<>();
        for (Long i : a) x.add(i);
        Collections.sort(x);
        for (int i = 0; i < a.length; ++i) a[i] = x.get(i);
    }

    public static void sort(ArrayList<Integer> arr) {Collections.sort(arr);}

    public static void pn(Object o){pw.println(o);}
        
    public static void p(Object o){pw.print(o);}
        
    public static void pni(Object o){pw.println(o);pw.flush();}

    static int gcd(int x , int y) {
        if (y == 0) return Math.abs(x);
        return gcd(y , x % y);
    }
}