Problem: A sequence of brackets is called balanced if one can turn it into a valid math expression by adding characters '+' and '1'. For example, sequences '(())()', '()', and '(()(()))' are balanced, while ')(', '(()', and '(()))(' are not.

You are given a binary string s of length n. Construct two balanced bracket sequences a and b of length n such that for all 1≤ i≤ n: 

  * if s_i=1, then a_i=b_i 
  * if s_i=0, then a_i≠ b_i 



If it is impossible, you should report about it.

Input

The first line contains a single integer t (1≤ t≤ 10^4) — the number of test cases.

The first line of each test case contains a single integer n (2≤ n≤ 2⋅ 10^5, n is even).

The next line contains a string s of length n, consisting of characters 0 and 1.

The sum of n across all test cases does not exceed 2⋅ 10^5.

Output

If such two balanced bracked sequences exist, output "YES" on the first line, otherwise output "NO". You can print each letter in any case (upper or lower).

If the answer is "YES", output the balanced bracket sequences a and b satisfying the conditions on the next two lines.

If there are multiple solutions, you may print any.

Example

Input


3
6
101101
10
1001101101
4
1100


Output


YES
()()()
((()))
YES
()()((()))
(())()()()
NO

Note

In the first test case, a="()()()" and b="((()))". The characters are equal in positions 1, 3, 4, and 6, which are the exact same positions where s_i=1.

In the second test case, a="()()((()))" and b="(())()()()". The characters are equal in positions 1, 4, 5, 7, 8, 10, which are the exact same positions where s_i=1.

In the third test case, there is no solution.

Solution (in JAVA):

Solution:
//package codeforces.problem.april;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.Objects;
import java.util.StringTokenizer;

/*
https://codeforces.com/problemset/problem/1503/A
 */
public class Task1503_A {

    static void solve() {
        int n = FS.nextInt();
        char[] s = FS.next().toCharArray();
        char[] a = new char[n], b = new char[n];

        int k = 0;
        for (int i = 0; i < n; i++) {
            if (s[i] == '1') {
                k++;
            }
        }

        if (k % 2 == 1 || s[0] != '1' || s[n-1] != '1') {
            FS.pt.println("NO");
            return;
        }

        FS.pt.println("YES");

        int usedK = 0;
        boolean flip = false;
        for (int i = 0; i < n; i++) {
            if (s[i] == '1') {
                if (usedK < k / 2) {
                    a[i] = '(';
                    b[i] = '(';
                    usedK++;
                } else {
                    a[i] = ')';
                    b[i] = ')';
                }
            } else {
                a[i] = flip ? '(' : ')';
                b[i] = flip ? ')' : '(';
                flip = !flip;
            }
        }

        FS.printArr(a);
        FS.printArr(b);
    }

    public static void main(String[] args) {
        int T = FS.nextInt();
        for (int tt = 0; tt < T; tt++) {
            solve();
        }
        FS.pt.close();
    }

    static class FS {
        private static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        private static StringTokenizer st = new StringTokenizer("");
        static PrintWriter pt = new PrintWriter(System.out);

        static String next() {
            while (!st.hasMoreTokens())
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        static int nextInt() {
            return Integer.parseInt(next());
        }

        static int[] readArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }

        static double nextDouble() {
            return Double.parseDouble(next());
        }

        static int[][] read2Array(int n, int m) {
            int[][] a = new int[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    a[i][j] = nextInt();
                }
            }
            return a;
        }

        static long[][] read2ArrayL(int n, int m) {
            long[][] a = new long[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    a[i][j] = nextLong();
                }
            }
            return a;
        }

        void printArr(long[] arr) {
            for (long value : arr) {
                pt.print(value);
                pt.print(" ");
            }
            pt.println();
        }

        static long[] readArrayL(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) a[i] = nextLong();
            return a;
        }

        static void printArr(int[] arr) {
            for (int value : arr) {
                pt.print(value);
                pt.print(" ");
            }
            pt.println();
        }

        static void printArr(char[] arr) {
            for (char value : arr) {
                pt.print(value);
            }
            pt.println();
        }

        static void printArrL(int[] arr) {
            for (int value : arr) {
                pt.print(value);
                pt.print(" ");
            }
            pt.println();
        }

        static void print2Arr(int[][] arr, int n, int m) {
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    pt.print(arr[i][j]);
                    pt.print(" ");
                }
                pt.println();
            }
            pt.println();
        }

        static void print2Arr(long[][] arr, int n, int m) {
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    pt.print(arr[i][j]);
                    pt.print(" ");
                }
                pt.println();
            }
            pt.println();
        }

        static List<Long> readListLong(int n) {
            List<Long> list = new ArrayList<>(n);
            for (int i = 0; i < n; i++) {
                list.add(nextLong());
            }
            return list;
        }

        static List<Integer> readListInt(int n) {
            List<Integer> list = new ArrayList<>(n);
            for (int i = 0; i < n; i++) {
                list.add(nextInt());
            }
            return list;
        }

        static <T> void printList(List<T> list) {
            for (T value : list) {
                pt.print(value);
                pt.print(" ");
            }
            pt.println();
        }

        static void close() {
            pt.close();
        }

        static long nextLong() {
            return Long.parseLong(next());
        }
    }

    static class Mat {
        public static long pow(long a, long exp) {
            return (long) Math.pow(a, exp);
        }
    }

    static class NumberTheory {
        public static boolean isPrime(long n) {
            if (n <= 1) return false;
            if (n < 4) return true;
            if (n % 2 == 0) return false;
            if (n % 3 == 0) return false;

            for (int i = 5, next = 2; i * i <= n; i += next, next = 6 - next)
                if (n % i == 0) return false;

            return true;
        }

        public static long gcd(long a, long b) {
            while (b != 0) {
                long tmp = a % b;
                a = b;
                b = tmp;
            }
            return a;
        }

        public static long lcm(long a, long b) {
            return a * b / gcd(a, b);
        }

        public static List<Long> primeFactors(long n) {
            List<Long> ans = new ArrayList<>();
            while (n % 2 == 0) {
                ans.add(2L);
                n /= 2;
            }

            // n must be odd at this point.  So we can
            // skip one element (Note i = i + 2)
            for (long i = 3; i <= Math.sqrt(n); i += 2) {
                // While i divides n, print i and divide n
                while (n % i == 0) {
                    ans.add(i);
                    n /= i;
                }
            }

            // This condition is to handle the case when
            // n is a prime number greater than 2
            if (n > 2) {
                ans.add(n);
            }
            return ans;
        }

        static long fact(long n) {
            if (n == 0 || n == 1) return 1L;
            long r = 1;
            for (int i = 1; i <= n; i++) {
                r *= i;
            }
            return r;
        }

        static long fact(long n, long mod) {
            if (n <= 1) return 1;
            long ans = 1;
            for (int i = 1; i <= n; i++) {
                ans = (ans * i) % mod;
            }
            return ans;
        }

        static long fastExp(long x, long n, long mod) {
            long ans = 1;
            while (n > 0) {
                if (n % 2 == 1) ans = (ans * x) % mod;
                x = (x * x) % mod;
                n /= 2;
            }
            return ans;
        }
    }

    static class BinarySearch {
        public static int lowerBound(int[] arr, int key) {
            int low = 0;
            int high = arr.length - 1;
            while (low < high) {
                int mid = low + (high - low) / 2;
                if (arr[mid] >= key) {
                    high = mid;
                } else {
                    low = mid + 1;
                }
            }
            return low;
        }

        public static int lowerBound(long[] arr, long key) {
            int low = 0;
            int high = arr.length - 1;
            while (low < high) {
                int mid = low + (high - low) / 2;
                if (arr[mid] >= key) {
                    high = mid;
                } else {
                    low = mid + 1;
                }
            }
            return low;
        }

        public static <T extends Comparable<T>> int lowerBound(List<T> arr, T key) {
            int low = 0;
            int high = arr.size() - 1;
            while (low < high) {
                int mid = low + (high - low) / 2;
                if (arr.get(mid).compareTo(key) >= 0) {
                    high = mid;
                } else {
                    low = mid + 1;
                }
            }
            return low;
        }

        public static int upperBound(int[] arr, int key) {
            int low = 0;
            int high = arr.length - 1;
            while (low < high) {
                int mid = low + (high - low + 1) / 2;
                if (arr[mid] <= key) {
                    low = mid;
                } else {
                    high = mid - 1;
                }
            }
            return low;
        }

        public static int upperBound(long[] arr, long key) {
            int low = 0;
            int high = arr.length - 1;
            while (low < high) {
                int mid = low + (high - low + 1) / 2;
                if (arr[mid] <= key) {
                    low = mid;
                } else {
                    high = mid - 1;
                }
            }
            return low;
        }

        public static <T extends Comparable<T>> int upperBound(List<T> arr, T key) {
            int low = 0;
            int high = arr.size() - 1;
            while (low < high) {
                int mid = low + (high - low + 1) / 2;
                if (arr.get(mid).compareTo(key) >= 0) {
                    low = mid;
                } else {
                    high = mid - 1;
                }
            }
            return low;
        }
    }

    static class Pair<T, K> {
        T first;
        K second;

        public Pair(T first, K second) {
            this.first = first;
            this.second = second;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Pair<?, ?> pair = (Pair<?, ?>) o;
            return Objects.equals(first, pair.first) &&
                    Objects.equals(second, pair.second);
        }

        @Override
        public int hashCode() {
            return Objects.hash(first, second);
        }
    }
}