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
for _ in range(int(input())):
    n=int(input())
    s=str(input())
    """x1="1"
    x1+=((n-1)*"0")
    x2="1"
    for i in range(1,n):
        x2+=s[i]
    l1=list(s)
    l2=list(x1)
    l3=list(x2)
    if(l1[0]=="1"):
        l2[0]="2"
        l3[0]="2"
    elif(l1[0]=="2"):
        l2[0]="1"
        l3[0]="1"
    
    #print(l2,l3)
    for i in l2:
        print(int(i),end="")
    print()
    for i in l3:
        print(int(i),end="")
    print()"""
    
    s1="1"
    s2="1"
    f=0
    g=0
    for i in range(n):
        if(s[i]=="1"):
            x=i
            g=1
            break
    
    for i in range(1,n):
        if(g==0):
            if(s[i]=="0"):
                s1+="0"
                s2+="0"
            else:
                s1+="1"
                s2+="1"
        else:
            if(i<x):
                if(s[i]=="0"):
                    s1+="0"
                    s2+="0"
                else:
                    s1+="1"
                    s2+="1"
            elif(i==x):
                s1+="1"
                s2+="0"
            else:
                if(s[i]=="0"):
                    s1+="0"
                    s2+="0"
                elif(s[i]=="1"):
                    s1+="0"
                    s2+="1"
                else:
                    s1+="0"
                    s2+="2"
                    
            
    print(s1)
    print(s2)
        
        