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.math.*;
import java.util.*;

public class test {

	public static void main(String[] args) {
		int test = fs.nextInt();
		for (int cases = 0; cases < test; cases++) {
			int n = fs.nextInt();
			String as = fs.next();
			char ar[] = as.toCharArray();
			char ar1[] = new char[n];
			char ar2[] = new char[n];
			ar1[0] = '1';
			ar2[0] = '1';
			int lastidof2 = 0;
			int lastidof1 = -1;
			int lastidof0 = -1;
			boolean one = false;
			for (int i = 1; i < n; i++) {
				char x = ar[i];
				if (x == '0') {
					ar1[i] = '0';
					ar2[i] = '0';
				} else if (x == '1' && !one) {
					one = true;
					ar1[i] = '1';
					ar2[i] = '0';
				} else if (x == '1' && one) {
					ar1[i] = '0';
					ar2[i] = '1';
				} else if (x == '2') {
					if (!one) {
						ar1[i] = '1';
						ar2[i] = '1';
					}
					else
					{
						ar1[i]='0';
						ar2[i]='2';
					}
				}
			}
			String s1 = "";
			String s2 = "";
			for (char c : ar1) {
				s1 += c;
			}
			for (char c : ar2) {
				s2 += c;
			}
			System.out.println(s1 + " " + s2);
		}

	}

	/*
	 * array list
	 * 
	 * ArrayList<Integer> al=new ArrayList<>(); creating BigIntegers
	 * 
	 * BigInteger a=new BigInteger(); BigInteger b=new BigInteger();
	 * 
	 * hash map
	 * 
	 * HashMap<Integer,Integer> hm=new HashMap<Integer,Integer>(); for(int
	 * i=0;i<ar.length;i++) { Integer c=hm.get(ar[i]); if(hm.get(ar[i])==null) {
	 * hm.put(ar[i],1); } else { hm.put(ar[i],++c); } }
	 * 
	 * while loop
	 * 
	 * int t=sc.nextInt(); while(t>0) { t--; }
	 * 
	 * array input
	 * 
	 * int n = sc.nextInt(); int ar[] = new int[n]; for (int i = 0; i < ar.length;
	 * i++) { ar[i] = sc.nextInt(); }
	 */
	static class Node {
		Node left, right;
		int data;

		public Node(int data) {
			this.data = data;
		}

		public void insert(int val) {
			if (val <= data) {
				if (left == null) {
					left = new Node(val);
				} else {
					left.insert(val);
				}
			} else {
				if (right == null) {
					right = new Node(val);
				} else {
					right.insert(val);
				}
			}
		}

		public boolean contains(int val) {
			if (data == val) {
				return true;
			} else if (val < data) {
				if (left == null) {
					return false;
				} else {
					return left.contains(val);
				}
			} else {
				if (right == null) {
					return false;
				} else {
					return right.contains(val);
				}
			}
		}

		public void inorder() {
			if (left != null) {
				left.inorder();
			}
			System.out.print(data + " ");
			if (right != null) {
				right.inorder();
			}
		}

		public int maxDepth() {
			if (left == null)
				return 0;
			if (right == null)
				return 0;
			else {
				int ll = left.maxDepth();
				int rr = right.maxDepth();
				if (ll > rr)
					return (ll + 1);
				else
					return (rr + 1);
			}
		}

		public int countNodes() {
			if (left == null)
				return 1;
			if (right == null)
				return 1;
			else {
				return left.countNodes() + right.countNodes() + 1;
			}
		}

		public void preorder() {
			System.out.print(data + " ");
			if (left != null) {
				left.inorder();
			}

			if (right != null) {
				right.inorder();
			}

		}

		public void postorder() {
			if (left != null) {
				left.inorder();
			}

			if (right != null) {
				right.inorder();
			}
			System.out.print(data + " ");

		}

		public void levelorder(Node node) {
			LinkedList<Node> ll = new LinkedList<Node>();
			ll.add(node);
			getorder(ll);

		}

		public void getorder(LinkedList<Node> ll) {
			while (!ll.isEmpty()) {
				Node node = ll.poll();
				System.out.print(node.data + " ");
				if (node.left != null)
					ll.add(node.left);
				if (node.right != null)
					ll.add(node.right);
			}
		}
	}

	static 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;
		}
	}

	static class Pair {
		int first, second;

		public Pair(int first, int second) {
			this.first = first;
			this.second = second;
		}

	}

	static class OutputWriter {
		private final PrintWriter writer;

		public OutputWriter(OutputStream outputStream) {
			writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
		}

		public OutputWriter(Writer writer) {
			this.writer = new PrintWriter(writer);
		}

		public void print(Object... objects) {
			for (int i = 0; i < objects.length; i++) {
				if (i != 0)
					writer.print(' ');
				writer.print(objects[i]);
			}
		}

		public void printLine(Object... objects) {
			print(objects);
			writer.println();
		}

		public void close() {
			writer.close();
		}

		public void flush() {
			writer.flush();
		}

	}

	private static final Scanner sc = new Scanner(System.in);
	private static final FastReader fs = new FastReader();
	private static final OutputWriter op = new OutputWriter(System.out);

	static int[] getintarray(int n) {
		int ar[] = new int[n];
		for (int i = 0; i < n; i++) {
			ar[i] = fs.nextInt();
		}
		return ar;
	}

	static long[] getlongarray(int n) {
		long ar[] = new long[n];
		for (int i = 0; i < n; i++) {
			ar[i] = fs.nextLong();
		}
		return ar;
	}

	static int[][] get2darray(int n, int m) {
		int ar[][] = new int[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				ar[i][j] = fs.nextInt();
			}
		}
		return ar;
	}

	static Pair[] getpairarray(int n) {
		Pair ar[] = new Pair[n];
		for (int i = 0; i < n; i++) {
			ar[i] = new Pair(fs.nextInt(), fs.nextInt());
		}
		return ar;
	}

	static void printarray(int ar[]) {
		for (int i : ar) {
			op.print(i + " ");
		}
		op.flush();
	}

	static int fact(int n) {
		int fact = 1;
		for (int i = 2; i <= n; i++) {
			fact *= i;
		}
		return fact;
	}

//	

	// function to find largest prime factor

}/*
	 * 1 5 -2 -3 -1 -4 -6till here
	 */

//		while (t > 0) {
//			int a[] = getintarray(3);
//			int b[] = getintarray(3);
//			int ans = getans(a, b);
//			System.out.println(ans);
//		}