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
/*
    Aman Agarwal
    algo.java
*/

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

public class C
{
    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 FastReader sc = new FastReader();
    static PrintWriter out = new PrintWriter(System.out);
    static int ni()throws IOException{return sc.nextInt();}
    static long nl()throws IOException{return sc.nextLong();}
    static int[] nai(int N,int start)throws IOException{int[]A=new int[N+start];for(int i=start;i!=(N+start);i++){A[i]=ni();}return A;}
    static Integer[] naI(int N,int start)throws IOException{Integer[]A=new Integer[N+start];for(int i=start;i!=(N+start);i++){A[i]=ni();}return A;}
    static long[] nal(int N)throws IOException{long[]A=new long[N];for(int i=0;i!=N;i++){A[i]=nl();}return A;}
    static void print(int arr[]){for(int i=0;i<arr.length;i++)out.print(arr[i]+" ");out.println();}
    static void print(long arr[]){for(int i=0;i<arr.length;i++)out.print(arr[i]+" ");out.println();}
    static long gcd(long a, long b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int gcd(int a, int b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int bit(long n)throws IOException{return (n==0)?0:(1+bit(n&(n-1)));} // return the number of set bits.
    static boolean isPrime(int number){if(number==1) return false;if (number == 2 || number == 3){return true;}if (number % 2 == 0) {return false;}int sqrt = (int) Math.sqrt(number) + 1;for(int i = 3; i < sqrt; i += 2){if (number % i == 0){return false;}}return true;}
    static boolean isPrime(long number){if(number==1) return false;if (number == 2 || number == 3){return true;}if (number % 2 == 0) {return false;}long sqrt = (long) Math.sqrt(number) + 1;for(int i = 3; i < sqrt; i += 2){if (number % i == 0){return false;}}return true;}
    static int power(int n,int p){if(p==0)return 1;int a = power(n,p/2);a = a*a;int b = p & 1;if(b!=0){a =  n*a;}return a;}
    static long power(long n,long p){if(p==0)return 1;long a = power(n,p/2);a = a*a;long b = p & 1;if(b!=0){a =  n*a;}return a;}
    static void reverse(int[] a) {int b;for (int i = 0, j = a.length - 1; i < j; i++, j--) {b = a[i];a[i] = a[j];a[j] = b;}}
    static void reverse(long[] a) {long b;for (int i = 0, j = a.length - 1; i < j; i++, j--) {b = a[i];a[i] = a[j];a[j] = b;}}
    static void swap(int a[],int i,int j){int temp = a[i];a[i] = a[j];a[j] = temp;}
    static void swap(long a[],int i,int j){long temp = a[i];a[i] = a[j];a[j] = temp;}
    static int count(int n){int c=0;while(n>0){c++;n = n/10;}return c;}
    static int[] prefix_sum(int a[],int n){int s[] = new int[n];s[0] = a[0];for(int i=1;i<n;i++){s[i] = a[i]+s[i-1];}return s;}
    static long[] prefix_sum_int(int a[],int n){long s[] = new long[n];s[0] = (long)a[0];for(int i=1;i<n;i++){s[i] = ((long)a[i])+s[i-1];}return s;}
    static long[] prefix_sum_Integer(Integer a[],int n){long s[] = new long[n];s[0] = (long)a[0];for(int i=1;i<n;i++){s[i] = ((long)a[i])+s[i-1];}return s;}
    static long[] prefix_sum_long(long a[],int n){long s[] = new long[n];s[0] = a[0];for(int i=1;i<n;i++){s[i] = a[i]+s[i-1];}return s;}
    static boolean isPerfectSquare(double x){double sr = Math.sqrt(x);return ((sr - Math.floor(sr)) == 0);}
    static ArrayList<Integer> sieve(int n) {int k=0; boolean prime[] = new boolean[n+1];ArrayList<Integer> p_arr = new ArrayList<>();for(int i=0;i<n;i++) prime[i] = true;for(int p = 2; p*p <=n; p++){ k=p;if(prime[p] == true) { p_arr.add(p);for(int i = p*2; i <= n; i += p) prime[i] = false; } }for(int i = k+1;i<=n;i++){if(prime[i]==true)p_arr.add(i);}return p_arr;} 
    static boolean[] seive_check(int n) {boolean prime[] = new boolean[n+1];for(int i=0;i<n;i++) prime[i] = true;for(int p = 2; p*p <=n; p++){ if(prime[p] == true) { for(int i = p*2; i <= n; i += p) prime[i] = false; } }prime[1]=false;return prime;} 
    static int get_bits(int n){int p=0;while(n>0){p++;n = n>>1;}return p;}
    static int get_bits(long n){int p=0;while(n>0){p++;n = n>>1;}return p;}
    static int get_2_power(int n){if((n & (n-1))==0)return get_bits(n)-1;return -1;}
    static int get_2_power(long n){if((n & (n-1))==0)return get_bits(n)-1;return -1;}
    static void close(){out.flush();}

    /*-------------------------Main Code Starts(algo.java)----------------------------------*/    

    public static void main(String[] args) throws IOException 
    {
        int t = 1;
        t = sc.nextInt();
        while(t-- > 0)
        {
            int n = ni();
            String s = sc.next();
            StringBuffer sb1 = new StringBuffer("");
            StringBuffer sb2 = new StringBuffer(""); 
            int cnt=0;
            for(int i=0;i<n;i++)
            {
                if(s.charAt(i)=='0')
                {
                    sb1.append("0");
                    sb2.append("0");
                }
                else if(s.charAt(i)=='2')
                {
                    if(cnt==0)
                    {
                        sb1.append("1");
                        sb2.append("1");
                    }
                    else
                    {
                        sb1.append("0");
                        sb2.append("2");
                    }
                }
                else
                {
                    if(cnt==0)
                    {
                        sb1.append("1");
                        sb2.append("0");
                        cnt++;
                    }
                    else
                    {
                        sb1.append("0");
                        sb2.append("1");
                    }
                }
            } 

            out.println(sb1);
            out.println(sb2);
        }
        close();
    }
}
