1382_C2. Prefix Flip (Hard Version)
This is the hard version of the problem. The difference between the versions is the constraint on n and the required number of operations. You can make hacks only if all versions of the problem are solved.

There are two binary strings a and b of length n (a binary string is a string consisting of symbols 0 and 1). In an operation, you select a prefix of a, and simultaneously invert the bits in the prefix (0 changes to 1 and 1 changes to 0) and reverse the order of the bits in the prefix.

For example, if a=001011 and you select the prefix of length 3, it becomes 011011. Then if you select the entire string, it becomes 001001.

Your task is to transform the string a into b in at most 2n operations. It can be proved that it is always possible.

Input

The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next 3t lines contain descriptions of test cases.

The first line of each test case contains a single integer n (1≤ n≤ 10^5) — the length of the binary strings.

The next two lines contain two binary strings a and b of length n.

It is guaranteed that the sum of n across all test cases does not exceed 10^5.

Output

For each test case, output an integer k (0≤ k≤ 2n), followed by k integers p_1,…,p_k (1≤ p_i≤ n). Here k is the number of operations you use and p_i is the length of the prefix you flip in the i-th operation.

Example

Input


5
2
01
10
5
01011
11100
2
01
01
10
0110011011
1000110100
1
0
1


Output


3 1 2 1
6 5 2 5 3 1 2
0
9 4 1 2 10 4 1 2 1 5
1 1

Note

In the first test case, we have 01→ 11→ 00→ 10.

In the second test case, we have 01011→ 00101→ 11101→ 01000→ 10100→ 00100→ 11100.

In the third test case, the strings are already the same. Another solution is to flip the prefix of length 2, which will leave a unchanged.
```python
t=int(input())
for _ in range(t):
    n=int(input())
    arr=list(input().rstrip("\n"))
    arr1=list(input().rstrip("\n"))
    arr=[int(x) for x in arr]
    arr1=[int(x) for x in arr1]
    #print(arr,n)
    result=[]
    if arr == arr1:
        print(0)
    else:
        if n == 1:
            print("1 1")
            continue
        prev=arr[0]
        for i in range(1,n):
            #print(arr,n)
            if prev != arr[i]:
                result.append(i)
            prev=arr[i]
        if arr[-1] == 1:
            last=1
        else:
            last=0
        for i in range(n-1,-1,-1):
            if arr1[i]!= last:
                result.append(i+1)
                if last == 0:
                    last=1
                else:
                    last=0
        print(len(result),end=" ")
        print(*result)
        
```