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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.util.*;

public class C {
	private static final FastReader fs = new FastReader();
	private static final PrintWriter out = new PrintWriter(System.out);

	private static void solve() {
		char[] line = fs.next().toCharArray();
		ArrayDeque<Character> q1 = new ArrayDeque<>(),q2 = new ArrayDeque<>();
		int first = 0,second = 0;
		for(char x : line) {
			if(x == ')' || x == ']') {
				if(x == ')') {
					if(q1.isEmpty())
						;
					else {
						first += 1;
						q1.removeLast();
					}
				}else {
					if(q2.isEmpty())
						;
					else {
						second += 1;
						q2.removeLast();
					}
				}
			}
			else {
				if(x == '(') {
					q1.add(x);
				}
				else {
					q2.add(x);
				}
			}
		}
		out.println(first+second);
	}

	public static void main(String[] args) {
		Thread t = new Thread(null, null, "", 1 << 28) {
			public void run() {
				int test_case = 1;
				test_case = fs.nextInt();
				for (int cs = 1; cs <= test_case; cs++) {
					solve();
				}
				out.close();
			}
		};
		t.start();
		try {
			t.join();
		} catch (InterruptedException e) {
			e.printStackTrace();
		}
	}

	private 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;
		}

		int[] readintarray(int n) {
			int res[] = new int[n];
			for (int i = 0; i < n; i++)
				res[i] = nextInt();
			return res;
		}

		long[] readlongarray(int n) {
			long res[] = new long[n];
			for (int i = 0; i < n; i++)
				res[i] = nextLong();
			return res;
		}
	}

	private static class cf {
		public static int min(int x, int y) {
			return Math.min(x, y);
		}

		public static int max(int x, int y) {
			return Math.max(x, y);
		}

		public static long min(long x, long y) {
			return Math.min(x, y);
		}

		public static long max(long x, long y) {
			return Math.max(x, y);
		}

		public static int abs(int x) {
			return x >= 0 ? x : -x;
		}

		public static long abs(long x) {
			return x >= 0 ? x : -x;
		}

		public static boolean even(int x) {
			return x % 2 == 0 ? true : false;
		}

		public static boolean even(long x) {
			return x % 2 == 0 ? true : false;
		}

		public static int power(int base, int exponent) {
			int res = 1;
			while (exponent > 0) {
				if (!even(exponent))
					res *= base;
				exponent >>= 1;
				base *= base;
			}
			return res;
		}

		public static long power(long base, long exponent) {
			long res = 1;
			while (exponent > 0) {
				if (!even(exponent))
					res *= base;
				exponent >>= 1;
				base *= base;
			}
			return res;
		}

		public static long mul(long a, long b, long mod) {
			return (a % mod * b % mod) % mod;
		}

		public static long add(long a, long b, long mod) {
			return (a % mod + b % mod) % mod;
		}

		public static long sub(long a, long b, long mod) {
			return ((a % mod - b % mod) % mod + mod) % mod;
		}

		public static long power(long base, long exponent, long mod) {
			long res = 1;
			base %= mod;
			while (exponent > 0) {
				if (!even(exponent))
					res = mul(res, base, mod);
				exponent >>= 1;
				base = mul(base, base, mod);
			}
			return res;
		}
	}
}