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:
//package codeforces;

import java.util.Scanner;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.TreeMap;
import java.util.TreeSet;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.Set;

public class q {
	// Integer.bitCount(i); count no of 1 bit in a given number
	static Scanner scn = new Scanner(System.in);
	//static int min=Integer.MAX_VALUE;
		static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}

	static FastReader s = new FastReader();
		
	static int mod = 1000000007;

	public static void main(String[] args) {
		// System.out.format("%.10f", ans);char c = sc.next().charAt(0);
		// code
		
		String str=scn.next();
		int n=str.length(),count=0;
		if(n%2==1)
		System.out.println("Impossible");
		else
		{
		boolean bl=true;
		Stack<Character>stk=new Stack<Character>();
		for(int i=0;i<n;i++)
		{
			if(str.charAt(i)=='{'||str.charAt(i)=='['||str.charAt(i)=='('||str.charAt(i)=='<')
				stk.push(str.charAt(i));
			else 
			{
				if(stk.isEmpty())
				{
					bl=false;
					break;
				}
				else if(!stk.isEmpty()&&(str.charAt(i)==')'&&stk.peek()=='(')||(str.charAt(i)=='}'&&stk.peek()=='{')||(str.charAt(i)==']'&&stk.peek()=='[')||(str.charAt(i)=='>'&&stk.peek()=='<'))
				{
					stk.pop();
				}
				else 
				{
					stk.pop();
					count++;
				}
			}
		}
		
		if(!bl||!stk.isEmpty())
			System.out.println("Impossible");
		else
			System.out.println(count);
		}

	}
	
	public static boolean[] sieveOfEratosthenes(int n) {

		boolean prime[] = new boolean[n + 1];
		for (int i = 0; i < n; i++)
			prime[i] = true;

		for (int p = 2; p * p <= n; p++) {
			// If prime[p] is not changed, then it is a prime
			if (prime[p] == true) {
				// Update all multiples of p
				for (int i = p * p; i <= n; i += p)
					prime[i] = false;
			}
		}

		for (int i = 2; i <= n; i++) {
			if (prime[i] == true) {
				// list.add(i);
			}

		}
		return prime;
	}

	public static class Pair implements Comparable {
		int x;
		int y;
		int z;

		Pair(int x, int y, int z) {
			this.x = x;
			this.y = y;
			this.z = z;
		}

		public int compareTo(Object o) {
			Pair pp = (Pair) o;
			if (pp.x == x)
				return 0;
			else if (x > pp.x)
				return 1;
			else
				return -1;
		}

	}

}