Problem: You are given a string s, consisting of brackets of two types: '(', ')', '[' and ']'.

A string is called a regular bracket sequence (RBS) if it's of one of the following types: 

  * empty string; 
  * '(' + RBS + ')'; 
  * '[' + RBS + ']'; 
  * RBS + RBS. 



where plus is a concatenation of two strings.

In one move you can choose a non-empty subsequence of the string s (not necessarily consecutive) that is an RBS, remove it from the string and concatenate the remaining parts without changing the order.

What is the maximum number of moves you can perform?

Input

The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of testcases.

Each of the next t lines contains a non-empty string, consisting only of characters '(', ')', '[' and ']'. The total length of the strings over all testcases doesn't exceed 2 ⋅ 10^5.

Output

For each testcase print a single integer — the maximum number of moves you can perform on a given string s.

Example

Input


5
()
[]()
([)]
)]([
)[(]


Output


1
2
2
0
1

Note

In the first example you can just erase the whole string.

In the second example you can first erase the brackets on positions 1 and 2: "[]()", then "()" is left. After that you can erase it whole. You could erase the whole string from the beginning but you would get one move instead of two.

In the third example you can first erase the brackets on positions 1 and 3: "([)]". They form an RBS "()". Then "[]" is left, so you can erase it whole.

In the fourth example there is no subsequence that is an RBS, so you can't perform a move at all.

In the fifth example you can erase the brackets on positions 2 and 4: ")[(]" and get ")(" as a result. You can erase nothing from it.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
public class prob3
{
    /**
     *
     */
    static PrintWriter out=new PrintWriter((System.out));
    static long maxx;
    public static void main(String args[])throws IOException
    {
        Reader sc=new Reader();
        int t=sc.nextInt();
        while(t-- >0){
            char[] s=sc.next().toCharArray();
            Map<Character,Integer> map=new HashMap<Character,Integer>();
            int num=0;
            for(char c:s){
                if(c=='(' || c=='[') map.put(c,map.getOrDefault(c, 0)+1);
                else{
                    if(c==')'){
                        if(map.containsKey('(')){
                            num++;
                            map.put('(',map.get('(')-1);
                            if(map.get('(')==0) map.remove('(');
                        }
                    }else{
                        if(map.containsKey('[')){
                            num++;
                            map.put('[',map.get('[')-1);
                            if(map.get('[')==0) map.remove('[');
                        }
                    }
                }
            }
            out.println(num);
            
        }
        
    	out.close();
 
    }
   
    /*
    private static void sieve(ArrayList<Integer> primes){
        int[] arr=new int[10000005];
        Arrays.fill(arr,1);
        arr[0]=0;
        arr[1]=0;
        for(int i=2;i*i<10000000;i++){
            if(arr[i]==1){
                for(int j=i*i;j<10000000;j+=i){
                    arr[j]=0;
                }
            }
        }
        primes.add(2);
        for(int i=3;i<10000000;i++){
            if(arr[i]==1) primes.add(i);
        }

    }

    */
        
    /*
    int n=sc.nextInt();
        	char[] s=sc.next().toCharArray();
        	int res=0;
        	for(int i=1;i<n;i++){
        		if( (s[i]=='1') && s[i]==s[i-1]) res++;
        	}
        	out.println(res);
    */
    
 
    public static long pow(long a,long b){
        if(b==0){
            return 1;
        }
        if(b%2==0){
            return pow(a*a,b/2);
        }else{
            return a*pow(a*a,b/2);
        }
    }
    static class Reader 
    { 
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");
        public String next()
        {
            while(!st.hasMoreTokens())
            {
                try
                {
                    st=new StringTokenizer(br.readLine());
                }
                catch(Exception e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        public int nextInt()
        {
            return Integer.parseInt(next());
        }
        public long nextLong()
        {
            return Long.parseLong(next());
        }
        public double nextDouble()
        {
            return Double.parseDouble(next());
        }
        public String nextLine()
        {
            try
            {
                return br.readLine();
            }
            catch(Exception e)
            {
                e.printStackTrace();
            }
            return null;
        }
        public boolean hasNext()
        {
            String next=null;
            try
            {
                next=br.readLine();
            }
            catch(Exception e)
            {
            }
            if(next==null)
            {
                return false;
            }
            st=new StringTokenizer(next);
            return true;
        }
    } 
}