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 CPP):

Solution:
#include <bits/stdc++.h>
char str[100005];
char str2[100005];
int solution[2 * 100005];
int steps, n;
int start, end, flipped;
void init() {
  start = 0;
  end = n - 1;
  flipped = 0;
  for (int i = 0; i < n; ++i) {
    str[i] -= '0';
    str2[i] -= '0';
  }
}
void useLast() {
  if (flipped) {
    start++;
  } else {
    end--;
  }
}
int getLast() {
  if (flipped) {
    return 1 - str[start];
  } else {
    return str[end];
  }
}
int getFirst() {
  if (flipped) {
    return 1 - str[end];
  } else {
    return str[start];
  }
}
void flip() { flipped = 1 - flipped; }
void solve() {
  steps = 0;
  init();
  int a, b;
  for (int j = n - 1; j >= 0; j--) {
    b = str2[j];
    if (b != getLast()) {
      a = getFirst();
      if (a == b) {
        solution[steps++] = 1;
      }
      solution[steps++] = j + 1;
      flip();
    }
    useLast();
  }
  printf("%d", steps);
  for (int i = 0; i < steps; ++i) {
    printf(" %d", solution[i]);
  }
  printf("\n");
}
int main() {
  int t;
  scanf("%d", &t);
  while (t--) {
    scanf("%d", &n);
    scanf("%s", str);
    scanf("%s", str2);
    solve();
  }
  return 0;
}