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.File;
import java.io.IOException;
import java.util.Scanner;

public final class Main
{
	public static void main(String[] args) throws IOException
	{
		Scanner in = getScan(args);

		int t = in.nextInt();
		in.nextLine();
		while (t-- > 0)
		{
			in.nextLine();
			String x = in.nextLine();
			StringBuffer a = new StringBuffer();
			StringBuffer b = new StringBuffer();
			boolean first = true;
			for (int i = 0; i < x.length(); i++)
			{
				switch (x.charAt(i))
				{
					case '0':
						a.append('0');
						b.append('0');
						break;
					case '1':
						if (first)
						{
							a.append('1');
							b.append('0');
							first = false;
						}
						else
						{
							a.append('0');
							b.append('1');
						}
						break;
					default:
						if (first)
						{
							a.append('1');
							b.append('1');
						}
						else
						{
							a.append('0');
							b.append('2');
						}
				}
			}
			System.out.println(a);
			System.out.println(b);
		}
	}

	static Scanner getScan(String[] args) throws IOException
	{
		if (args.length == 0)
		{
			return new Scanner(System.in);
		}
		else
		{
			return new Scanner(new File(args[0]));
		}
	}
}
