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.math.*;
import java.math.BigInteger; 
//import javafx.util.*; 
public final class B
{    
	static StringBuilder ans=new StringBuilder();
	static FastReader in=new FastReader();
	static ArrayList<ArrayList<Integer>> g,CARS,intersection;	
	static long mod=1000000007;
	static int D1[],D2[],par[];
	static boolean set[];
	static long INF=Long.MAX_VALUE;
	static int dp[][];
	public static void main(String args[])throws IOException
	{  		
		int T=i();
		outer:while(T-->0)
		{
			int N=i();
			char X[]=in.next().toCharArray();
			int cnt=0;
			for(char x:X)if(x=='1')cnt++;
			int a=0,b=0,open=0; boolean flag=true;
			char A[]=new char[N];
			char B[]=new char[N];
			if(X[0]=='0' || X[N-1]=='0')
			{
				System.out.println("NO");
				continue outer;
			}
			for(int i=0; i<N; i++)
			{
				char x=X[i];
				if(x=='1')
				{
					if(open*2<cnt)
					{
						A[i]='(';
						B[i]='(';						
					}
					else
					{
						A[i]=')';
						B[i]=')';
					}
					open++;
				}
				else
				{
					if(flag)
					{
						A[i]='(';
						B[i]=')';
					}
					else
					{
						A[i]=')';
						B[i]='(';
					}
					flag^=true;
				}
			}
			//print(A); print(B);
			if(f(A) && f(B))
			{
				ans=new StringBuilder();
				System.out.println("YES");
				for(char x:A)ans.append(x);
				ans.append("\n");
				for(char x:B)ans.append(x);
				System.out.println(ans);
			}
			else System.out.println("NO");

		}
	}
	static boolean f(char A[])
	{
		int c=0;
		for(int i=0; i<A.length; i++)
		{
			if(A[i]=='(')c++;
			else
			{
				if(c==0)return false;
				else c--;
			}
		}
		if(c>0)return false;
		return true;
	}
	static boolean f(char A[],char B[])
	{
		int c=0;
		for(int i=0; i<A.length; i++)if(A[i]==B[i])c++;
		if(c==A.length)return false;
		return true;
	}
	static int[] merge(int A[],int B[],int N)
	{
		int C[]=new int[N*2];
		int i=0,j=0,index=0;
		while(i<N && j<N)
		{
			if(A[i]<B[i])C[index++]=A[i++];
			else C[index++]=B[j++];
		}
		while(i<N)C[index++]=A[i++];
		while(j<N)C[index++]=B[j++];
		return C;
	}
	static boolean valid(int A[])
	{
		for(int i=1; i<=A.length; i++)
		{
			if(A[i-1]!=i)return false;
		}
		return true;
	}
	static void f(int A[],int i,int j)
	{
		while(i<j)
		{
			//swap i & j
			int t=A[i];
			A[i]=A[j];
			A[j]=t;
			i++;
			j--;
		}
		//print(A);
	}
	static boolean valid(long a,long b,long c)
	{
		if(a<=c && b>=c)return true;
		return false;
	}
	static boolean ispalin(char X[],int l,int r)
	{
		while(l<r)
		{
			if(X[l]!=X[r])return false;
			l++; r--;
		}
		return true;
	}

	static long min(long a,long b,long c)
	{
		return Math.min(a, Math.min(c, b));
	}
	static void dfs(int n)
	{
		set[n]=true;
		for(int c:g.get(n))
		{
			if(!set[c])dfs(c);
		}
	}
	static void print(int a)
	{
		System.out.println("! "+a);
	}
	static int ask(int a,int b)
	{
		System.out.println("? "+a+" "+b);
		return i();
	}
	static int find(int a)
	{
		if(par[a]<0)return a;
		return par[a]=find(par[a]);
	}
	static void union(int a,int b)
	{
		a=find(a);
		b=find(b);
		if(a!=b)
		{
			par[a]+=par[b]; //transfers the size
			par[b]=a;       //changes the parent
		}
	}
	static ArrayList<Integer> IND(int B[],HashMap<Integer,Integer> mp)
	{
		ArrayList<Integer> A=new ArrayList<>();
		for(int i:B)
		{
			if(mp.containsKey(i))
			{
				A.add(i);
				int f=mp.get(i)-1;
				if(f==0)
					mp.remove(i);
				else mp.put(i, f);		
			}
		}
		return A;
	}
	static HashMap<Integer,Integer> hash(int A[],int index)
	{
		HashMap<Integer,Integer> mp=new HashMap<Integer,Integer>();
		for(int i=index; i<A.length; i++)
		{
			int f=mp.getOrDefault(A[i], 0)+1;
			mp.put(A[i], f);
		}
		return mp;
	}
	static void swap(char A[],int a,int b)
	{
		char ch=A[a];
		A[a]=A[b];
		A[b]=ch;
	}

	static long lower_Bound(long A[],int low,int high, long x) 
	{ 
		if (low > high) 
			if (x >= A[high]) 
				return A[high]; 

		int mid = (low + high) / 2; 

		if (A[mid] == x) 
			return A[mid]; 

		if (mid > 0 && A[mid - 1] <= x && x < A[mid]) 
			return A[mid - 1]; 

		if (x < A[mid]) 
			return lower_Bound( A, low, mid - 1, x); 

		return lower_Bound(A, mid + 1, high, x); 
	} 
	static void sort(long[] a) //check for long
	{
		ArrayList<Long> l=new ArrayList<>();
		for (long i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}
	static void setGraph(int N)
	{
		g=new ArrayList<ArrayList<Integer>>();
		intersection=new ArrayList<ArrayList<Integer>>();
		CARS=new ArrayList<ArrayList<Integer>>();
		for(int i=0; i<=N; i++)
		{
			CARS.add(new ArrayList<Integer>());
			intersection.add(new ArrayList<Integer>());
			g.add(new ArrayList<Integer>());

		}
	}

	static  long pow(long a,long b)
	{
		long mod=1000000007;
		long pow=1;
		long x=a;
		while(b!=0)
		{
			if((b&1)!=0)pow=(pow*x)%mod;
			x=(x*x)%mod;
			b/=2;
		}
		return pow;
	}
	static long toggleBits(long x)//one's complement || Toggle bits
	{
		int n=(int)(Math.floor(Math.log(x)/Math.log(2)))+1;

		return ((1<<n)-1)^x;
	}
	static int countBits(long a)
	{
		return (int)(Math.log(a)/Math.log(2)+1);
	}
	static void sort(int[] a) {
		ArrayList<Integer> l=new ArrayList<>();
		for (int i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}
	static boolean isPrime(long 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 long GCD(long a,long b) 
	{
		if(b==0)
		{
			return a;
		}
		else return GCD(b,a%b );
	}

	//Debugging Functions Starts

	static void print(char A[])
	{
		for(char c:A)System.out.print(c+" ");
		System.out.println();
	}
	static void print(boolean A[])
	{
		for(boolean c:A)System.out.print(c+" ");
		System.out.println();
	}
	static void print(int A[])
	{
		for(int a:A)System.out.print(a+" ");
		System.out.println();	
	}
	static void print(long A[])
	{
		for(long i:A)System.out.print(i+ " ");
		System.out.println();

	}
	static void print(ArrayList<Integer> A)
	{
		for(int a:A)System.out.print(a+" ");
		System.out.println();
	}

	//Debugging Functions END
	//----------------------
	//IO FUNCTIONS STARTS
	static HashMap<Integer,Integer> Hash(int A[])
	{
		HashMap<Integer,Integer> mp=new HashMap<>();
		for(int a:A)
		{
			int f=mp.getOrDefault(a,0)+1;
			mp.put(a, f);
		}
		return mp;
	}
	static int i()
	{
		return in.nextInt();
	}

	static long l()
	{
		return in.nextLong();
	}

	static int[] input(int N){
		int A[]=new int[N];
		for(int i=0; i<N; i++)
		{
			A[i]=in.nextInt();
		}
		return A;
	}

	static long[] inputLong(int N)     {
		long A[]=new long[N];
		for(int i=0; i<A.length; i++)A[i]=in.nextLong();
		return A;
	}

	//IO FUNCTIONS END

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

//Code For FastReader
//Code For FastReader
//Code For FastReader
//Code For FastReader
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;
	}

}