A number is ternary if it contains only digits 0, 1 and 2. For example, the following numbers are ternary: 1022, 11, 21, 2002.

You are given a long ternary number x. The first (leftmost) digit of x is guaranteed to be 2, the other digits of x can be 0, 1 or 2.

Let's define the ternary XOR operation ⊙ of two ternary numbers a and b (both of length n) as a number c = a ⊙ b of length n, where c_i = (a_i + b_i) \% 3 (where \% is modulo operation). In other words, add the corresponding digits and take the remainders of the sums when divided by 3. For example, 10222 ⊙ 11021 = 21210.

Your task is to find such ternary numbers a and b both of length n and both without leading zeros that a ⊙ b = x and max(a, b) is the minimum possible.

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases. Then t test cases follow. The first line of the test case contains one integer n (1 ≤ n ≤ 5 ⋅ 10^4) — the length of x. The second line of the test case contains ternary number x consisting of n digits 0, 1 or 2. It is guaranteed that the first digit of x is 2. It is guaranteed that the sum of n over all test cases does not exceed 5 ⋅ 10^4 (∑ n ≤ 5 ⋅ 10^4).

Output

For each test case, print the answer — two ternary integers a and b both of length n and both without leading zeros such that a ⊙ b = x and max(a, b) is the minimum possible. If there are several answers, you can print any.

Example

Input


4
5
22222
5
21211
1
2
9
220222021


Output


11111
11111
11000
10211
1
1
110111011
110111010
import java.io.*;
import java.util.*;

public class test {

	
	public static void main(String[] args) throws IOException {
		// TODO Auto-generated method stub
		Reader.init(System.in);
		int t=Reader.nextInt();
		while(t-->0) {
			int n=Reader.nextInt();
			String x=Reader.next();
			char arr[]=x.toCharArray();
			String a="1";
			String b="1";
			int j=Integer.MAX_VALUE;
			for(int i=1;i<n;i++) {
				int num=arr[i]-48;
				if(num==2) {
					if(i>j) {
						a+='0';
						b+='2';
						continue;
					}
					a+='1';
					b+='1';
					
					
				}
				else if(num==1) {
//					if(a.compareToIgnoreCase(b)>0) {
//						a+="0";
//						b+="1";
//					}
//					else {
//						a+="1";
//						b+="0";
//					}
					if(i>j) {
						a+='0';
						b+='1';
						continue;
					}
					a+='1';
					b+='0';
					j=i;
					
				}
				else if(num==0) {
					a+=0;b+=0;
					
				}
			}
			System.out.println(a);
			System.out.println(b);
			
			
		}
			



}
}





class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;
 
    /** call this method to initialize reader for InputStream */
    static void init(InputStream input) {
        reader = new BufferedReader(
                     new InputStreamReader(input) );
        tokenizer = new StringTokenizer("");
    }
 
    /** get next word */
    static String next() throws IOException {
        while ( ! tokenizer.hasMoreTokens() ) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                   reader.readLine() );
        }
        return tokenizer.nextToken();
    }
    static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }
	
    static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }
}
