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:
#!/usr/bin/env python
import os
import operator
import sys
from _collections import defaultdict
import bisect
from io import BytesIO, IOBase

def inar():
    return [int(k) for k in input().split()]
def power(x, p,m):
    res = 1
    while p:
        if p & 1:
            res = (res * x) % m
        x = (x * x) % m
        p >>= 1
    return res
visited=[]
level=[]
adj=defaultdict(list)
def bfs(node):
    global visited, level, adj
    qu=[]
    visited[node]=1
    qu.append(node)
    while qu:
        el=qu.pop(0)
        for child in adj[el]:
            if not visited[child]:
                level[child]=level[el]+1
                visited[child]=1
                qu.append(child)


def main():
    #mod=1000000007
    # global visited, level, adj
    # #for _ in range(int(input())):
    # #n=int(input())
    # n,m,k=map(int,input().split())
    # arr=inar()
    # for i in range(m):
    #     u,v=map(int,input().split())
    #     adj[u].append(v)
    #     adj[v].append(u)
    # level=[0]*(n+1)
    # visited=[0]*(n+1)
    # bfs(1)
    # print(level[n])
    for _ in range(int(input())):
        n=int(input())
        s=input()
        t=input()
        s+="0"
        t+="0"
        res=[]
        for i in range(n):
            if s[i]!=s[i+1]:
                res.append(i+1)
        for i in range(n-1,-1,-1):
            if t[i]!=t[i+1]:
                res.append(i+1)
        print(len(res),end=" ")
        print(*res)


    # string=input()
    # n=len(string)
    # ans=[]
    # for i in range(26):
    #     lis=[0]*26
    #     ans.append(lis)
    # temp=[0]*26
    # result=0
    # for i in range(0,n):
    #     temp[ord(string[i])-97]+=1
    # for i in range(26):
    #     result=max(result,temp[i])
    # temp=[0]*26
    # temp[ord(string[0])-97]+=1
    #
    # for i in range(1,n):
    #     val=ord(string[i])-97
    #     for j in range(26):
    #         ans[val][j]+=temp[j]
    #     temp[val]+=1
    # # for i in range(26):
    # #     print(*ans[i])
    # for i in range(26):
    #     for j in range(26):
    #         result=max(result,ans[i][j])
    # print(result)




















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")

if __name__ == "__main__":
    main()