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.*;
import javafx.util.Pair;
import java.math.*;
import java.math.BigInteger;
import java.util.LinkedList; 
import java.util.Queue; 
public final  class CodeForces
{    
    static StringBuilder ans=new StringBuilder();
    static FastReader in=new FastReader();
    static ArrayList<ArrayList<Integer>> g;
    static long mod=1000000007;
    static boolean set[];   
    static Pair<Integer,Integer> seg[];
    static int A[];
    public static void main(String args[])throws IOException
    {
        int T=i();
        while(T-->0)
        {
            Stack<Integer> a=new Stack<>();
            Stack<Integer> b=new Stack<>();
            String X=in.next();
            int c=0;
            for(int i=0; i<X.length(); i++)
            {
                if(X.charAt(i)=='(')a.push(1);
                if(X.charAt(i)=='[')b.push(1);
                if(X.charAt(i)==')')
                {
                    if(a.size()>0)
                    {
                        c++;
                        a.pop();
                    }
                }
                if(X.charAt(i)==']')
                {
                    if(b.size()>0)
                    {
                        c++;
                        b.pop();
                    }
                }
            }
            ans.append(c+"\n");
        }System.out.println(ans);
    }

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

    static String swap(String X,int i,int j)
    {
        char ch[]=X.toCharArray();
        char a=ch[i];
        ch[i]=ch[j];
        ch[j]=a;
        return new String(ch);
    }

    static int sD(long n)  
    {  

        if (n % 2 == 0 )  
            return 2;  

        for (int i = 3; i * i <= n; i += 2) {  
            if (n % i == 0 )  
                return i;  
        }  

        return (int)n;  
    }  

    static void setGraph(int N)
    {
        set=new boolean[N+1];
        g=new ArrayList<ArrayList<Integer>>();
        for(int i=0; i<=N; i++)
            g.add(new ArrayList<Integer>());
    }

    static void DFS(int N,int d)
    {
        set[N]=true;
        d++;
        for(int i=0; i<g.get(N).size(); i++)
        {
            int c=g.get(N).get(i);
            if(set[c]==false)
            {
                DFS(c,d);
            }
        }
    }

    static  long pow(long a,long b)
    {
        long mod=1000000007;
        long pow=1;
        long x=a;
        while(b!=0)
        {
            if((b&1)!=0)pow=(pow*x)%mod;
            x=(x*x)%mod;
            b/=2;
        }
        return pow;
    }

    static long toggleBits(long x)//one's complement || Toggle bits
    {
        int n=(int)(Math.floor(Math.log(x)/Math.log(2)))+1;

        return ((1<<n)-1)^x;
    }

    static int countBits(long a)
    {
        return (int)(Math.log(a)/Math.log(2)+1);
    }

    static long fact(long N)
    { 
        long n=2; 
        if(N<=1)return 1;
        else
        {
            for(int i=3; i<=N; i++)n=(n*i)%mod;
        }
        return n;
    }

    static int kadane(int A[])
    {
        int lsum=A[0],gsum=A[0];
        for(int i=1; i<A.length; i++)
        {
            lsum=Math.max(lsum+A[i],A[i]);
            gsum=Math.max(gsum,lsum);
        }
        return gsum;
    }

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

    static boolean isPrime(long N)
    {
        if (N<=1)  return false; 
        if (N<=3)  return true; 
        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; 
    }

    static int i()
    {
        return in.nextInt();
    }

    static long l()
    {
        return in.nextLong();
    }

    static int[] input(int N){
        int A[]=new int[N];
        for(int i=0; i<N; i++)
        {
            A[i]=in.nextInt();
        }
        return A;
    }

    static long[] inputLong(int N)     {
        long A[]=new long[N];
        for(int i=0; i<A.length; i++)A[i]=in.nextLong();
        return A;
    }

    static long GCD(long a,long b) 
    {
        if(b==0)
        {
            return a;
        }
        else return GCD(b,a%b );
    }

}
//Code For FastReader
//Code For FastReader
//Code For FastReader
//Code For FastReader
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;
    }

}