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.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.ArrayList;
import java.util.Random;
import java.util.Stack;
import java.util.StringTokenizer;

public class BalanceTheBits {
	
	static final int MAXN = 1000_006;
	
	static final long MOD = (long) 1e9 + 7;
	
	public static void main(String[] args) throws IOException {
		MyScanner s = new MyScanner();
		Print p = new Print();
		int t = s.nextInt();
		
		while (t-- > 0) {
			
			int n = s.nextInt();
			char[] arr = s.nextLine().toCharArray();
			
			int zc = 0;
			int oc = 0;
			for (int i = 0; i < n; i++) {
				if (arr[i] == '0')
					zc++;
				else
					oc++;
			}
			
			StringBuilder sb1 = new StringBuilder();
			StringBuilder sb2 = new StringBuilder();
			
			boolean sol = true;
			
			if (arr[0] == '0' || arr[n - 1] == '0' || zc % 2 != 0) {
				p.println("NO");
				continue;
			}
			int k = 0;
			int cha = 0;
			for (int i = 0; i < n; i++) {
				if (arr[i] == '1') {
					char ch = k < oc / 2 ? '(' : ')';
					sb1.append(ch);
					sb2.append(ch);
					k++;
				} else {
					sb1.append(cha == 0 ? ')' : '(');
					sb2.append(cha == 0 ? '(' : ')');
					cha ^= 1;
					
				}
			}
			p.println("YES");
			p.println(sb1.toString());
			p.println(sb2.toString());
		}
		
		p.close();
	}
	
	public static class Pair implements Comparable<Pair> {
		
		int first;
		
		int second;
		
		public Pair(int a, int b) {
			this.first = a;
			this.second = b;
		}
		
		@Override
		public int hashCode() {
			final int prime = 31;
			int result = 1;
			result = prime * result + first;
			result = prime * result + second;
			return result;
		}
		
		@Override
		public boolean equals(Object obj) {
			if (this == obj)
				return true;
			if (obj == null)
				return false;
			if (getClass() != obj.getClass())
				return false;
			Pair other = (Pair) obj;
			if (first != other.first)
				return false;
			if (second != other.second)
				return false;
			return true;
		}
		
		@Override
		public int compareTo(Pair o) {
			// TODO Auto-generated method stub
			return o.first - first;
		}
		
	}
	
	public static class Helper {
		
		long MOD = (long) 1e9 + 7;
		
		int MAXN = 1000_006;;
		
		Random rnd;
		
		public Helper(long mod, int maxn) {
			MOD = mod;
			MAXN = maxn;
			rnd = new Random();
		}
		
		public Helper() {
			
		}
		
		public static int[] sieve;
		
		public static ArrayList<Integer> primes;
		
		public void setSieve() {
			primes = new ArrayList<>();
			sieve = new int[MAXN];
			int i, j;
			for (i = 2; i < MAXN; ++i)
				if (sieve[i] == 0) {
					primes.add(i);
					for (j = i; j < MAXN; j += i) {
						sieve[j] = i;
					}
				}
		}
		
		public static long[] factorial;
		
		public void setFactorial() {
			factorial = new long[MAXN];
			factorial[0] = 1;
			for (int i = 1; i < MAXN; ++i)
				factorial[i] = factorial[i - 1] * i % MOD;
		}
		
		public long getFactorial(int n) {
			if (factorial == null)
				setFactorial();
			return factorial[n];
		}
		
		public long ncr(int n, int r) {
			if (r > n)
				return 0;
			if (factorial == null)
				setFactorial();
			long numerator = factorial[n];
			long denominator = factorial[r] * factorial[n - r] % MOD;
			return numerator * pow(denominator, MOD - 2, MOD) % MOD;
		}
		
		public long[] getLongArray(int size, MyScanner s) throws Exception {
			long[] ar = new long[size];
			for (int i = 0; i < size; ++i)
				ar[i] = s.nextLong();
			return ar;
		}
		
		public int[] getIntArray(int size, MyScanner s) throws Exception {
			int[] ar = new int[size];
			for (int i = 0; i < size; ++i)
				ar[i] = s.nextInt();
			return ar;
		}
		
		public int[] getIntArray(String s) throws Exception {
			s = s.trim().replaceAll("\\s+", " ");
			String[] strs = s.split(" ");
			int[] arr = new int[strs.length];
			for (int i = 0; i < strs.length; i++) {
				arr[i] = Integer.parseInt(strs[i]);
			}
			return arr;
		}
		
		public long gcd(long a, long b) {
			return b == 0 ? a : gcd(b, a % b);
		}
		
		public int gcd(int a, int b) {
			return b == 0 ? a : gcd(b, a % b);
		}
		
		public long max(long[] ar) {
			long ret = ar[0];
			for (long itr : ar)
				ret = Math.max(ret, itr);
			return ret;
		}
		
		public int max(int[] ar) {
			int ret = ar[0];
			for (int itr : ar)
				ret = Math.max(ret, itr);
			return ret;
		}
		
		public long min(long[] ar) {
			long ret = ar[0];
			for (long itr : ar)
				ret = Math.min(ret, itr);
			return ret;
		}
		
		public int min(int[] ar) {
			int ret = ar[0];
			for (int itr : ar)
				ret = Math.min(ret, itr);
			return ret;
		}
		
		public long sum(long[] ar) {
			long sum = 0;
			for (long itr : ar)
				sum += itr;
			return sum;
		}
		
		public long sum(int[] ar) {
			long sum = 0;
			for (int itr : ar)
				sum += itr;
			return sum;
		}
		
		public long pow(long base, long exp, long MOD) {
			base %= MOD;
			long ret = 1;
			while (exp > 0) {
				if ((exp & 1) == 1)
					ret = ret * base % MOD;
				base = base * base % MOD;
				exp >>= 1;
			}
			return ret;
		}
		
	}
	
	static class Print {
		
		private BufferedWriter bw;
		
		public Print() {
			this.bw = new BufferedWriter(new OutputStreamWriter(System.out));
		}
		
		public void print(Object object) throws IOException {
			bw.append("" + object);
		}
		
		public void println(Object object) throws IOException {
			print(object);
			bw.append("\n");
		}
		
		public void close() throws IOException {
			bw.close();
		}
	}
	
	public static class MyScanner {
		
		BufferedReader br;
		
		StringTokenizer st;
		
		public MyScanner() {
			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;
		}
	}
	
}