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 sys,bisect
from math import gcd
input = sys.stdin.readline

############ ---- USER DEFINED INPUT FUNCTIONS ---- ############
def inp():
    return(int(input().rstrip()))
def inlt():
    return(list(map(int,input().rstrip().split())))
def insr():
    s = input().rstrip()
    return(s[:len(s) - 1])
def invr():
    return(map(int,input().rstrip().split()))
################################################################
############ ---- THE ACTUAL CODE STARTS BELOW ---- ############

t = inp()
for _ in range(t):
    n = inp()
    nums = [int(i) for i in input().strip()]
    a = [0 for i in range(n)]
    b = [0 for i in range(n)]
    a[0] = 1;b[0] = 1;has = False
    for i in range(1,n):
        if nums[i] == 0:
            a[i] = 0
            b[i] = 0
        elif nums[i] == 1:
            a[i] = 1
            b[i] = 0
            cnt = i
            has = True
            break
        else:
            a[i] = 1
            b[i] = 1

    if has:
        if cnt + 1< n:
            for i in range(cnt + 1,n):
                if nums[i] == 0:
                    a[i] = 0
                    b[i] = 0
                elif nums[i] == 1:
                    a[i] = 0
                    b[i] = 1
                else:
                    a[i] = 0
                    b[i] = 2
        

    print(''.join(str(i) for i in a))
    print(''.join(str(i) for i in b))
    
