human
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
Solve the task in PYTHON3.
 Write me a Python code 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?
assistant
#Here is Python code 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.

import sys, os, io
def rs(): return sys.stdin.readline().rstrip()
def ri(): return int(sys.stdin.readline())
def ria(): return list(map(int, sys.stdin.readline().split()))
def ws(s): sys.stdout.write(s + '\n')
def wi(n): sys.stdout.write(str(n) + '\n')
def wia(a): sys.stdout.write(' '.join([str(x) for x in a]) + '\n')
import math,datetime
from collections import deque
import collections

def main():
    starttime=datetime.datetime.now()
    
    if(os.path.exists('input.txt')):
        sys.stdin = open("input.txt","r")
        sys.stdout = open("output.txt","w")
    for _ in range(int(input())):
        n=int(input())
        x=input()
        a=""
        b=""
        for i in x:
            if i=='2':
                a+='1'
                b+='1'
            if i=='1':
                a+='0'
                b+='1'
            if i=='0':
                a+='0'
                b+='0'
        
        a,b=max(a,b),min(a,b)
        l=n
        # print("ORIGANLEE")
        # print(a)
        # print(b)
        for i in range(n):
            if a[i]!=b[i]:
                l=i
                break
                
        c=""
        d=""
        for i in range(l+1,n):
            k=str(ord(a[i])+ord(b[i])-96)
            c+='0'
            d+=k
        # print("MODIFIED")
        print(a[:l+1]+c)
        print(b[:l+1]+d)
                
                
                
        
                
        
            
            
            
            
            
        
        
        
        
    
            
                
                    
                        
        
                    
                    
        

    
    
    
    
    
    

    
    
                
class FastReader(io.IOBase):
    newlines = 0

    def __init__(self, fd, chunk_size=1024 * 8):
        self._fd = fd
        self._chunk_size = chunk_size
        self.buffer = io.BytesIO()

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size,...