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.math.BigInteger;
import java.util.*;
 
 
public class Main {
		public static void main(String[] args) throws IOException 
		{
		InputReader in = new InputReader(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		String s=in.readString();
		Stack<Character> ss=new Stack();
		char a[]=s.toCharArray();
		int ans=0;
		for(int i=0;i<s.length();i++)
		{
			if(a[i]=='('||a[i]=='{'||a[i]=='<'||a[i]=='[')
			{
				ss.push(a[i]);
			}
			else
			{
				if(ss.isEmpty())
				{
					System.out.println("Impossible");
					System.exit(0);
				}
				char c=ss.peek();
				ss.pop();
				if(c=='('&&a[i]!=')')
				{
					ans++;
				}
				if(c=='['&&a[i]!=']')
				{
					ans++;
				}
				if(c=='{'&&a[i]!='}')
				{
					ans++;
				}
				if(c=='<'&&a[i]!='>')
				{
					ans++;
				}
			}
		}
		if(!ss.isEmpty())
			System.out.println("Impossible");
		else
			System.out.println(ans);
		}
		
		public static long power(long a,long b)
		{
			long result=1;
			while(b>0)
			{
				if(b%2==1)
					result*=a;
				a=a*a;
				b/=2;
			}
			return result;
		}
		public static boolean isPrime(long n) 
		{
	        // Corner cases
	        if (n <= 1)
	            return false;
	        if (n <= 3)
	            return true;

	        // This is checked so that we can skip 
	        // middle five numbers in below loop
	        if (n % 2 == 0 || n % 3 == 0)
	            return false;

	        for (int i = 5; i * i <= n; i = i + 6)
	            if (n % i == 0 || n % (i + 2) == 0)
	                return false;

	        return true;
	    }
		public static long pow(long n,long p,long m)
	{
		 long  result = 1;
		  if(p==0)
		    return 1;
		if (p==1)
		    return n;
		while(p!=0)
		{
		    if(p%2==1)
		        result *= n;
		    if(result>=m)
		    result%=m;
		    p >>=1;
		    n*=n;
		    if(n>=m)
		    n%=m;
		}
		return result;
	}
	
 
 
	static class Pair implements Comparable<Pair>{
		int area;
		int price;
		Pair(int mr,int er){
			area=mr;price=er;
		}
		@Override
		public int compareTo(Pair o) {
			if(o.area>this.area)
				return 1;
			else if(o.area<this.area)
				return -1;
			else
			{
				if(o.price<this.price)
					return 1;
				else
					return -1;
			}
			}
	}
	public static long gcd(long a, long b) {
		  if (b == 0) return a;
		  return gcd(b, a%b);
		}
	static class InputReader {
 
		private InputStream stream;
		private byte[] buf = new byte[8192];
		private int curChar, snumChars;
		private SpaceCharFilter filter;
 
		public InputReader(InputStream stream) {
			this.stream = stream;
		}
 
		public int snext() {
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}
 
		public   int nextInt() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
 
		public long nextLong() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
 
		public int[] nextIntArray(int n) {
			int a[] = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}
 
		public String readString() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = snext();
			} while (!isSpaceChar(c));
			return res.toString();
		}
 
		public boolean isSpaceChar(int c) {
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
 
		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	}
}