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.util.Scanner;
import java.io.*;

public class ternary {

	public static void main(String[] args) {
		Scanner scn = new Scanner(System.in);
        int t = scn.nextInt();
        while(t!=0)
        {
        	int n = scn.nextInt();
        	String s=scn.next();
        	String a="";
        	String b ="";
        	int count=0;
        	for(int i =0;i<n;i++)
        	{
        		char ch = s.charAt(i);
        		
        		if(ch=='2' && count==0 )
        		{
        			a= a+"1";
        			b=b+"1";
        		}
        		
        		else if(ch=='1' && count==0)
        		{
        			a= a+"1";
        			b=b+"0";
        			count++;
        		}
        		else if(ch=='0')
        		{
        			
        			a= a+"0";
        			b=b+"0";
        		}
        		else if(ch=='2' && count>0)
        		{
        			a= a+"0";
        			b=b+"2";
        		}
        		else if(ch=='1' && count>0)
        		{
        			a= a+"0";
        			b=b+"1";
        		}
        	}
        	
        	System.out.println(a);
        	System.out.println(b);
        	t--;
        }

	}

}
