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 math
import sys,collections
from sys import stdin, stdout  
#MAXN = 10000001

def get_ints(): return map(int, sys.stdin.readline().strip().split())
def get_array(): return list(map(int, sys.stdin.readline().strip().split()))
def get_string(): return sys.stdin.readline().strip() 
def input(): return sys.stdin.readline().strip()
#spf = [0 for i in range(MAXN)] 
def file():
	sys.stdin = open('input.py', 'r')
	sys.stdout = open('output.py', 'w') 
def is_subsequence(x, y):
    """Test whether x is a subsequence of y"""
    x = list(x)
    for letter in y:
        if x and x[0] == letter:
            x.pop(0)

    return not x    
def sieve(): 
	spf[1] = 1
	for i in range(2, MAXN): 
		spf[i] = i 
	for i in range(4, MAXN, 2): 
		spf[i] = 2

	for i in range(3, mt.ceil(mt.sqrt(MAXN))): 
		if (spf[i] == i): 
			for j in range(i * i, MAXN, i): 
				if (spf[j] == j): 
					spf[j] = i 
def getFactorization(x): 
	ret = list() 
	while (x != 1): 
		ret.append(spf[x]) 
		x = x // spf[x] 

	return ret 
def getFloor(A, x):

    (left, right) = (0, len(A) - 1)

    ind,floor = -1,-1
    while left <= right:
        mid = (left + right) // 2
        '''if A[mid] == x:
            return mid'''
        if x < A[mid]:
            right = mid - 1
        else:
            floor = A[mid]
            ind=mid
            left = mid + 1
            
    return ind
def check(st) : 
  
    # Compute sum of digits 
    n = len(st) 
    digitSum = 0
      
    for i in range(0,n) : 
        digitSum = digitSum + (int)(st[i]) 
  
    # Check if sum of digits 
    # is divisible by 9. 
    return (digitSum % 9 == 0)     
def isPowerOfTwo(n): 
    if (n == 0): 
        return False
    while (n != 1): 
            if (n % 2 != 0): 
                return False
            n = n // 2
            
              
    return True
def kitte(n):
	c=0
	while(n!=0):
		n=n//2
		c+=1
	return c	
def aa(b,c):
	m=min(b,c)
	b-=m
	c-=m
	if(c>0 and b>0):
		return(m+((b+c)//3))
	else:
		return(m)
def bb(a,c):
	m=min(a,c)
	a-=m
	c-=m
	if(c>0 and a>0):
		return(m+((a+c)//3))
	else:
		return(m)
def cc(b,a):
	m=min(b,a)
	b-=m
	a-=m
	if(a>0 and b>0):
		return(m+((b+a)//3))
	else:
		return(m)		
def findProductSum(A, n): 
      
    # calculating array sum (a1 + a2 ... + an) 
    array_sum = 0
    for i in range(0, n, 1): 
        array_sum = (array_sum + A[i])
  
    # calcualting square of array sum 
    # (a1 + a2 + ... + an)^2 
    array_sum_square = (array_sum * array_sum)
  
    # calcualting a1^2 + a2^2 + ... + an^2 
    individual_square_sum = 0
    for i in range(0, n, 1): 
        individual_square_sum += (A[i] * A[i])
  
    # required sum is (array_sum_square - 
    # individual_square_sum) / 2 
    return (array_sum_square - 
            individual_square_sum) // 2		
def transpose(a):
	b=a[:][:]
	N=len(a)
	for i in range(N):
		for j in range(N):
			b[i][j] = a[j][i]
	return b        
def assign_rank_based_on_scores(a):
	final=[]
	for ii in a:
		temp=ii[:]
		l=[1]
		temp.sort(reverse=True)
		for j in range(1,len(temp)):
			if(temp[j]==temp[j-1]):
				l.append(l[-1])
			else:
				l.append(j+1)
		d=collections.defaultdict(int)
		j=0
		for i in temp:
			d[i]=l[j]
			j+=1
		ans=[]	
		for j in ii:
			ans.append(d[j])
		final.append(ans)	
	return(final)	
#file()
#sieve()

mod=(10**9)+7	
def main():
	
    n = int(input())
    s = input()
    a = ['1']
    b = ['1']
    flag = 0
    for i in range(1,n):
        if s[i] == '0':
            a.append('0')
            b.append('0')
        elif flag == 1 and s[i]=='1':
            a.append('1')
            b.append('0')
        elif flag == 0 and s[i]=='1':
            a.append('0')
            b.append('1')
            flag = 1
        elif flag == 0 and s[i]=='2':
            a.append('1')
            b.append('1')
            # flag = 1
        elif flag == 1 and s[i]=='2':
            a.append('2')
            b.append('0')
    print(''.join(a))
    print(''.join(b))
		



			
		


		



		



		
				










		
		




















	



	

	
			


		




		






		







			



	

	




	





















	




















		
			


		

			

		





			

	























				

	















	

	










if __name__ == '__main__':
	for tt in range(int(input())):
		main()
