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:
    /*
        Aman Agarwal
        algo.java
    */
     
    import java.util.*;
    import java.io.*;
     
    public class C
    {
        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 sc = new FastReader();
        static PrintWriter out = new PrintWriter(System.out);
        static int ni()throws IOException{return sc.nextInt();}
        static long nl()throws IOException{return sc.nextLong();}
        static int[][] nai2(int n,int m)throws IOException{int a[][] = new int[n][m];for(int i=0;i<n;i++)for(int j=0;j<m;j++)a[i][j] = ni();return a;}
        static int[] nai(int N,int start)throws IOException{int[]A=new int[N+start];for(int i=start;i!=(N+start);i++){A[i]=ni();}return A;}
        static Integer[] naI(int N,int start)throws IOException{Integer[]A=new Integer[N+start];for(int i=start;i!=(N+start);i++){A[i]=ni();}return A;}
        static long[] nal(int N)throws IOException{long[]A=new long[N];for(int i=0;i!=N;i++){A[i]=nl();}return A;}
        static char[] nac()throws IOException{char[]A=sc.next().toCharArray();return A;}
        static void print(int arr[]){for(int i=0;i<arr.length;i++)out.print(arr[i]+" ");out.println();}
        static void print(long arr[]){for(int i=0;i<arr.length;i++)out.print(arr[i]+" ");out.println();}
        static long gcd(long a, long b)throws IOException{return (b==0)?a:gcd(b,a%b);}
        static int gcd(int a, int b)throws IOException{return (b==0)?a:gcd(b,a%b);}
        static int bit(long n)throws IOException{return (n==0)?0:(1+bit(n&(n-1)));} // return the number of set bits.
        static boolean isPrime(int number){if(number==1) return false;if (number == 2 || number == 3){return true;}if (number % 2 == 0) {return false;}int sqrt = (int) Math.sqrt(number) + 1;for(int i = 3; i < sqrt; i += 2){if (number % i == 0){return false;}}return true;}
        static boolean isPrime(long number){if(number==1) return false;if (number == 2 || number == 3){return true;}if (number % 2 == 0) {return false;}long sqrt = (long) Math.sqrt(number) + 1;for(int i = 3; i < sqrt; i += 2){if (number % i == 0){return false;}}return true;}
        static int power(int n,int p){if(p==0)return 1;int a = power(n,p/2);a = a*a;int b = p & 1;if(b!=0){a =  n*a;}return a;}
        static long power(long n,long p){if(p==0)return 1;long a = power(n,p/2);a = a*a;long b = p & 1;if(b!=0){a =  n*a;}return a;}
        static void reverse(int[] a) {int b;for (int i = 0, j = a.length - 1; i < j; i++, j--) {b = a[i];a[i] = a[j];a[j] = b;}}
        static void reverse(long[] a) {long b;for (int i = 0, j = a.length - 1; i < j; i++, j--) {b = a[i];a[i] = a[j];a[j] = b;}}
        static void swap(int a[],int i,int j){a[i] = a[i] ^ a[j];a[j] = a[j] ^ a[i];a[i] = a[i] ^ a[j];}
        static void swap(long a[],int i,int j){a[i] = a[i] ^ a[j];a[j] = a[j] ^ a[i];a[i] = a[i] ^ a[j];}
        static int count(int n){int c=0;while(n>0){c++;n = n/10;}return c;}
        static int[] prefix_sum(int a[],int n){int s[] = new int[n];s[0] = a[0];for(int i=1;i<n;i++){s[i] = a[i]+s[i-1];}return s;}
        static long[] prefix_sum_int(int a[],int n){long s[] = new long[n];s[0] = (long)a[0];for(int i=1;i<n;i++){s[i] = ((long)a[i])+s[i-1];}return s;}
        static long[] prefix_sum_Integer(Integer a[],int n){long s[] = new long[n];s[0] = (long)a[0];for(int i=1;i<n;i++){s[i] = ((long)a[i])+s[i-1];}return s;}
        static long[] prefix_sum_long(long a[],int n){long s[] = new long[n];s[0] = a[0];for(int i=1;i<n;i++){s[i] = a[i]+s[i-1];}return s;}
        static boolean isPerfectSquare(double x){double sr = Math.sqrt(x);return ((sr - Math.floor(sr)) == 0);}
        static ArrayList<Integer> sieve(int n) {int k=0; boolean prime[] = new boolean[n+1];ArrayList<Integer> p_arr = new ArrayList<>();for(int i=0;i<n;i++) prime[i] = true;for(int p = 2; p*p <=n; p++){ k=p;if(prime[p] == true) { p_arr.add(p);for(int i = p*2; i <= n; i += p) prime[i] = false; } }for(int i = k+1;i<=n;i++){if(prime[i]==true)p_arr.add(i);}return p_arr;} 
        static boolean[] seive_check(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] == true) { for(int i = p*2; i <= n; i += p) prime[i] = false; } }prime[1]=false;return prime;} 
        static int get_bits(int n){int p=0;while(n>0){p++;n = n>>1;}return p;}
        static int get_bits(long n){int p=0;while(n>0){p++;n = n>>1;}return p;}
        static int get_2_power(int n){if((n & (n-1))==0)return get_bits(n)-1;return -1;}
        static int get_2_power(long n){if((n & (n-1))==0)return get_bits(n)-1;return -1;}
        //gives the divisors of first n natural numbers in n*sqrt(n) time..
        static ArrayList<ArrayList<Integer>> divisors_n(int n){int i,j;ArrayList<ArrayList<Integer>> ans = new ArrayList<>();ArrayList<Integer> arr = new ArrayList<>();arr.add(1);ans.add(arr);for (i = 2; i <= n; i++){arr = new ArrayList<>();for (j = 1; j * j <= i; j++){if (i % j == 0){arr.add(j);if (i / j != j)arr.add(i/j);}}ans.add(arr);} return ans;} 
        //gives divisors of a particular number in sqrt(n) time..
        static ArrayList<Integer> divisors_1(int n){ArrayList<Integer> ans = new ArrayList<>();for (int i=1; i<=Math.sqrt(n); i++){if (n%i==0){if (n/i == i)ans.add(i);else{ans.add(i);ans.add(n/i);}}}return ans;} 
        static void close(){out.flush();}
     
        /*-------------------------Main Code Starts(algo.java)----------------------------------*/    
     
        public static void solve() throws IOException 
        {
            char c[] = sc.next().toCharArray();
            int n = c.length;
            int t1=-1;
            int t2=-1;
            int cnt=0;

            for(int i=0;i<n;i++)
            {
                if(c[i]=='(')
                {
                    if(t1==-1)
                        t1=1;
                    else
                        t1++;
                }
                else if(c[i]=='[')
                {
                    if(t2==-1)
                        t2=1;
                    else
                        t2++;
                }
                else if(c[i]==')')
                {
                    if(t1>0)
                    {
                        t1--;
                        cnt++;
                    }
                    if(t1==0)
                        t1=-1;
                }
                else
                {
                    if(t2>0)
                    {
                        t2--;
                        cnt++;
                    }
                    if(t2==0)
                        t2=-1;
                }
            }
            out.println(cnt);
        }
     
        public static void main(String[] args) throws IOException 
        {
            int test = 1;
            test = sc.nextInt();
            while(test-- > 0)
            {
                solve();
            }
            close();
        }
    }