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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.HashMap;
import java.util.Map;
import java.util.Stack;

public class test {
	/*
	 * 		int n = 0, p = 0, q = 0;
			String[] npq = br.readLine().split(" ");
			n = Integer.parseInt(npq[0]);
			p = Integer.parseInt(npq[1]);
			q = Integer.parseInt(npq[2]);
			String str = br.readLine();
	 */
	private static void findSplit(String s, int n, int p, int q) {
		for(int i=0; i*p<=n; i++) {
			if((n-i*p)%q != 0)
				continue;
			System.out.println((i+(n-i*p)/q));
			int cur = 0;
			for( ; cur<i*p; cur+=p)
				System.out.println(s.substring(cur, cur+p));
			for( ; cur<s.length(); cur+=q)
				System.out.println(s.substring(cur, cur+q));
			return;
		}
		System.out.println("-1");
	}
	
	/*
	 * 		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
			
			int n = Integer.parseInt(br.readLine());
			String[] ss = br.readLine().split(" ");
			int[] fps = new int[n];
			for(int i=0; i<n; i++)
				fps[i] = Integer.parseInt(ss[i]);
	 */
	private static void readSectors(int[] fps) {
		Map<Integer, Integer> map = new HashMap<>();
		for(int i=0; i<fps.length; i++)
			map.put(fps[i], i);
		long cost = 0;
		for(int i=2; i<=fps.length; i++)
			cost += (long)Math.abs(map.get(i)-map.get(i-1));
		System.out.println(cost);
	}
	
	private static void minReplaceForRBS(String s) {
		Stack<Character> stk = new Stack<>();
		int count = 0;
		for(int i=0; i<s.length(); i++) {
			char c = s.charAt(i);
			if("<{[(".indexOf(c) != -1) {
				stk.push(c);
			} else if(stk.isEmpty()) {
				System.out.println("Impossible");
				return;
			} else if(">}])".indexOf(c) != "<{[(".indexOf(stk.pop()))
				count++;
		}
		if(!stk.isEmpty())
			System.out.println("Impossible");
		else
			System.out.println(count);
	}
	
	public static void main(String[] args) {
		try{
			BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
			
			String s = br.readLine();
			minReplaceForRBS(s);
		}catch(IOException io){
			io.printStackTrace();
		}	
	}
}