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:
import java.io.*;
import java.util.*;
import java.lang.*;

public class Main {
    static final int MAXN = 100001; // sqrt of 10^9 ;
    static ArrayList<Integer> arr1 = new ArrayList<>();
    static int int_max = Integer.MAX_VALUE;
    static int[] spf = new int[MAXN];

    public static void main(String[] args) throws IOException {
        FastReader sc = new FastReader();
        int l = sc.nextInt();

        for (int t = 1; t <= l; t++) {
            int n = sc.nextInt();
            String s = sc.nextLine();
            StringBuilder a = new StringBuilder();
            StringBuilder b = new StringBuilder();
            boolean ok = false;
            int abc=0;
            int c0=0;

            if(s.charAt(0)=='0' || s.charAt(n-1)=='0')
            {
                ok=false;
            }
            else {
                for(int i=0;i<n;i++)
                {
                    if(s.charAt(i)=='0')
                        c0++;
                }
                if (c0 % 2 == 0) {
                    ok = true;
                    a.append('(');
                    b.append('(');
                    int a0 = 0, a1 = 0;
                    for (int i = 1; i < n - 1; i++) {
                        if (s.charAt(i) == '0') {
                            if (a0 % 2 == 0) {
                                a.append('(');
                                b.append(')');
                            } else {
                                a.append(')');
                                b.append('(');
                            }
                            a0++;
                        } else {
                            if (a1 % 2 == 0) {
                                a.append('(');
                                b.append('(');
                            } else {
                                a.append(')');
                                b.append(')');
                            }
                            a1++;
                        }
                    }
                    a.append(')');
                    b.append(')');
                }
            }

                if (!ok) {
                    System.out.println("NO");
                } else {
                    System.out.println("YES");
                    System.out.println(a);
                    System.out.println(b);
                }
            }


        }


    static long mod_inv(long a, long m) {
        long m0 = m, t, q;
        long x0 = 0, x1 = 1;

        if (m == 1)
            return 0;

        // Apply extended Euclid Algorithm
        while (a > 1) {
            // q is quotient
            q = a / m;

            t = m;

            // m is remainder now, process
            // same as euclid's algo
            m = a % m;
            a = t;

            t = x0;

            x0 = x1 - q * x0;

            x1 = t;
        }

        // Make x1 positive
        if (x1 < 0)
            x1 += m0;

        return x1;
    } //(a*res)%m==1

    static long power(long x, long y) {
        long res = 1;
        while (y > 0) {
            if ((y & 1) == 1)
                res = res * x;

            y = y >> 1; // y = y/2
            x = x * x;
        }
        return res;
    } //return x^y;

    static int fact(int n) {
        int res = 1;
        for (int i = 2; i <= n; i++)
            res = res * i;
        return res;
    }

    static int ceilSearch(int[] arr, int low, int high, int x) {
        int mid;

        if (x <= arr[low])
            return low;
        if (x > arr[high])
            return -1;

        mid = (low + high) / 2;
        if (arr[mid] == x)
            return mid;
        else if (arr[mid] < x) {
            if (mid + 1 <= high && x <= arr[mid + 1])
                return mid + 1;
            else
                return ceilSearch(arr, mid + 1, high, x);
        } else {
            if (mid - 1 >= low && x > arr[mid - 1])
                return mid;
            else
                return ceilSearch(arr, low, mid - 1, x);
        }
    }

    static int floorSearch(int[] arr, int low, int high, int x) {
        // If low and high cross each other
        if (low > high)
            return -1;

        // If last element is smaller than x
        if (x >= arr[high])
            return high;

        // Find the middle point
        int mid = (low + high) / 2;

        // If middle point is floor.
        if (arr[mid] == x)
            return mid;

        // If x lies between mid-1 and mid
        if (
                mid > 0 && arr[mid - 1] <= x && x < arr[mid])
            return mid - 1;

        // If x is smaller than mid, floor
        // must be in left half.
        if (x < arr[mid])
            return floorSearch(
                    arr, low,
                    mid - 1, x);

        // If mid-1 is not floor and x is
        // greater than arr[mid],
        return floorSearch(
                arr, mid + 1, high,
                x);
    }

    static void sieve() {
        spf[1] = 1;
        for (int i = 2; i < MAXN; i++)
            spf[i] = i;
        for (int i = 4; i < MAXN; i += 2)
            spf[i] = 2;

        for (int i = 3; i * i < MAXN; i++) {
            if (spf[i] == i) {
                for (int j = i * i; j < MAXN; j += i)
                    if (spf[j] == j)
                        spf[j] = i;
            }
        }
    } //spf

    static ArrayList<Integer> getFactorization(int x) {
        sieve();
        ArrayList<Integer> ret = new ArrayList<>();
        while (x != 1) {
            ret.add(spf[x]);
            x = x / spf[x];
        }
        return ret;
    }

    static ArrayList<Integer> sieveOfEratosthenes(int n) {
        ArrayList<Integer> arr = new ArrayList<Integer>();
        boolean[] prime = new boolean[n + 1];
        Arrays.fill(prime, true);
        for (int p = 2; p * p <= n; p++) {
            if (prime[p]) {
                for (int i = p * p; i <= n; i += p)
                    prime[i] = false;
            }
        }
        for (int i = 2; i <= n; i++) {
            if (prime[i])
                arr.add(i);
        }
        return arr;
    }

    static boolean isPrime(int 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 funhelpfulforsegmented(int[] primes, int numprimes) {

        primes[numprimes++] = 2;

        for (int i = 3; i <= 32000; i += 2) {
            boolean isprime = true;
            double cap = Math.sqrt(i) + 1.0;

            for (int j = 0; j < numprimes; j++) {
                if (j >= cap) break;
                if (i % primes[j] == 0) {
                    isprime = false;
                    break;
                }
            }
            if (isprime) primes[numprimes++] = i;
        }
        return numprimes;
    }

    static ArrayList<Integer> segmentedsieve(int M, int N) {
        int[] primes = new int[4000];
        int numprimes = 0;
        numprimes = funhelpfulforsegmented(primes, numprimes);
        ArrayList<Integer> arr = new ArrayList<>();
        if (M < 2) M = 2;
        boolean[] isprime = new boolean[100001];
        for (int j = 0; j < 100001; j++) {
            isprime[j] = true;
        }

        for (int i = 0; i < numprimes; i++) {
            int p = primes[i];
            int start;

            if (p >= M) start = p * 2;
            else start = M + ((p - M % p) % p);

            for (int j = start; j <= N; j += p) {
                isprime[j - M] = false;
            }
        }
        for (int i = M; i <= N; i++) {
            if (isprime[i - M]) arr.add(i);
        }
        return arr;
    }

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

    public static int gcdExtended(int a, int b, int x, int y) {
        if (a == 0) {
            x = 0;
            y = 1;
            return b;
        }

        int x1 = 1, y1 = 1;
        int gcd = gcdExtended(b % a, a, x1, y1);
        x = y1 - (b / a) * x1;
        y = x1;
        return gcd;
    } // ax + by = gcd(a,b) ;

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

    static void prime_upto_10pow8() {
        boolean[] prime = new boolean[100000000];
        Arrays.fill(prime, true);
        int i;
        prime[1] = false;
        prime[0] = false;
        for (i = 4; i < 100000000; i += 2)
            prime[i] = false;

        prime[2] = true;
        for (i = 3; i * i < 100000000; i += 2) {
            if (prime[i])
                for (int j = i * i; j > 0 && j < 100000000; j = j + (2 * i))
                    prime[j] = false;
        }
        int[] arr = new int[8000000];
        int j = 0;
        arr[0] = 2;
        int n = 100000000;
        for (i = 3; i <= n; i += 2) {
            if (prime[i])
                arr[++j] = i;
        }
        for (i = 1; i <= j; i += 100) {
            System.out.println(arr[i - 1]);
        }
    }
    // int gcd of a nd b is gcdExtended(a, b, x, y);

    static class Pair {
        int a, b;

        Pair(int a, int b) {
            this.a = a;
            this.b = b;
        }
    }

    public 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;
        }
    }


}