Problem: This is the easy 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 3n 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≤ 1000) — 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 1000.

Output

For each test case, output an integer k (0≤ k≤ 3n), 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.

Solution (in PYTHON3):

Solution:
import os
import sys
from io import BytesIO, IOBase
import random
def main():
    t = int(input())
    for _ in range(t):
        n = int(input())
        a, b = input(), input()
        # n = 5
        # a = ''.join([random.choice(['1', '0']) for i in range(n)])
        # b = ''.join([random.choice(['1', '0']) for i in range(n)])

        # n = 5
        # a = '01101' 
        # b = '11001'
        # n = 5
        # a = '01111' 
        # b = '11111'

        if a == b:
            print(0)
            # print(a, b, 0)
            continue

        done = 0
        numops, preflens = 0, []
        while done!=n:
            if done == n-1:
                if a[0]!=b[0]:
                    numops += 1
                    preflens += [1]
                
                break

            if a[n-done-2:n-done] != b[n-done-2:n-done]:
                start = a[:2]
                end = b[n-done-2:n-done]
                # print(start, end, a[n-done-2:n-done], b[n-done-2:n-done])


                if end == '01':
                    if start == '11':
                        numops += 2
                        preflens += [1, n - done]
                    elif start == '00':
                        numops += 3
                        preflens += [2, 1, n - done]
                    elif start == '10':
                        numops += 4
                        preflens += [1, 2, 1, n-done]
                    else:
                        numops += 1
                        preflens += [n-done]

                    temp = '01' + a[2:n - done]
                    temp = temp.replace('0','2').replace('1', '0').replace('2', '1')
                    a = temp[::-1] + a[n-done:]

                if end == '11':
                    if start == '01':
                        numops += 3
                        preflens += [1, 2, n - done]
                    elif start == '10':
                        numops += 2
                        preflens += [1, n - done]
                    elif start == '00':
                        numops += 1
                        preflens += [n-done]
                    else:
                        numops += 2
                        preflens += [2, n-done]

                    temp = '00' + a[2:n - done]
                    temp = temp.replace('0','2').replace('1', '0').replace('2', '1')
                    a = temp[::-1] + a[n-done:]

                if end == '00':
                    if start == '10':
                        numops += 3
                        preflens += [1, 2, n - done]
                    elif start == '01':
                        numops += 2
                        preflens += [1, n - done]
                    elif start == '11':
                        numops += 1
                        preflens += [n-done]
                    else:
                        numops += 2
                        preflens += [2, n-done]

                    temp = '11' + a[2:n - done]
                    temp = temp.replace('0','2').replace('1', '0').replace('2', '1')
                    a = temp[::-1] + a[n-done:]

                if end == '10':
                    if start == '00':
                        numops += 2
                        preflens += [1, n - done]

                    elif start == '11':
                        numops += 3
                        preflens += [2, 1, n - done]
                    elif start == '01':
                        numops += 4
                        preflens += [1, 2, 1, n - done]
                    else:
                        numops += 1
                        preflens += [n-done]

                    temp = '10' + a[2:n - done]
                    temp = temp.replace('0','2').replace('1', '0').replace('2', '1')
                    a = temp[::-1] + a[n-done:]
                

            done += 2
                
        print(numops, *preflens)
        # print(a, b, numops, *preflens)
                
                
        




































# region fastio
BUFSIZE = 8192
class FastIO(IOBase):
    newlines = 0
    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None
 
    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()
 
    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()
 
    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)

class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
# endregion
 
if __name__ == "__main__":
    main()