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 Add {

    public static void main(String args[]) throws IOException {
        Scanner sc = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int t = sc.nextInt();
        while(t--!=0){
            String s = sc.next();
            int left1 = 0;
            int left2 = 0;
            int ans = 0;
            for(int i=0;i<s.length();i++){
                if(s.charAt(i)=='('){
                    left1++;
                }else if(s.charAt(i)=='['){
                    left2++;
                }else if(s.charAt(i)==')' && left1>0){
                    left1--;
                    ans++;
                }else if(s.charAt(i)==']' && left2>0){
                    left2--;ans++;
                }
                
            }
            pw.println(ans);
        }
        pw.close();
    }
    public static int gcd(int a,int b){
        int ans=1;
        for(int i = 1; i <= a && i <= a; i++)
        {
            if(a%i==0 && b%i==0)
                ans = i;
        }
        return ans;
    }
    static class Scanner {
	StringTokenizer st;
	BufferedReader br;
        
	public Scanner(InputStream s) {
		br = new BufferedReader(new InputStreamReader(s));
	}
        
	public Scanner(String file) throws FileNotFoundException {
		br = new BufferedReader(new FileReader(file));
        }
	public String next() throws IOException {
		while (st == null || !st.hasMoreTokens())
			st = new StringTokenizer(br.readLine());
		return st.nextToken();
	}
	public int nextInt() throws IOException {
		return Integer.parseInt(next());
	}

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

	public String nextLine() throws IOException {
		return br.readLine();
	}

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

	public boolean ready() throws IOException {
		return br.ready();
	}

    }
}