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 JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.math.*;

public class C658 {

    public static void main(String args[]) {
        FastReader sc = new FastReader();
        StringBuilder sb = new StringBuilder();
        int t, i, n, temp, j;
        t = sc.nextInt();
        while (t-- > 0) {
            n = sc.nextInt();
            String st = sc.next();
            String st2 = sc.next();
            int a[] = new int[n];
            int b[] = new int[n];
            for (i = 0; i < n; i++) {
                a[i] = st.charAt(i) - '0';
                b[i] = st2.charAt(i) - '0';
            }
            StringBuilder ans = new StringBuilder();
            int count = 0;
            int x = n - 1;
            for (x = n - 1; x >= 1; x--) {
                if (a[0] == b[x]) {
                    count++;
                    ans.append(1).append(' ');
                    a[0] = a[0] ^ 1;
                    count++;
                    ans.append(x + 1).append(' ');
                    int lim = x / 2;
                    if (x % 2 == 0)
                        lim = (x - 1) / 2;
                    for (j = 0; j <= lim; j++) {
                        a[j] = a[j] ^ 1;
                        a[x - j] = a[x - j] ^ 1;
                        temp = a[j];
                        a[j] = a[x - j];
                        a[x - j] = temp;
                    }
                    if (x % 2 == 0)
                        a[x / 2] = a[x / 2] ^ 1;
                } else {
                    count++;
                    ans.append(x + 1).append(' ');
                    int lim = x / 2;
                    if (x % 2 == 0)
                        lim = (x - 1) / 2;
                    for (j = 0; j <= lim; j++) {
                        a[j] = a[j] ^ 1;
                        a[x - j] = a[x - j] ^ 1;
                        temp = a[j];
                        a[j] = a[x - j];
                        a[x - j] = temp;
                    }
                    if (x % 2 == 0)
                        a[x / 2] = a[x / 2] ^ 1;
                }
            }
            if (a[0] != b[0]) {
                count++;
                a[0] = a[0] ^ 1;
                ans.append(1).append(' ');
            }
            if(ans.length()>0)
                ans.deleteCharAt(ans.length() - 1);
            sb.append(count).append(' ').append(ans).append('\n');
            // print(a,0,n-1);
        }
        sb.deleteCharAt(sb.length() - 1);
        out.println(sb);
    }

    static PrintWriter out;

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out, true);
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    public static boolean isPrime(int n) {
        if (n < 2)
            return false;
        for (int i = 2; i <= (int) Math.sqrt(n); i++) {
            if (n % i == 0)
                return false;
        }
        return true;
    }

    public static void print(int a[], int l, int r) {
        int i;
        for (i = l; i <= r; i++)
            out.print(a[i] + " ");
        out.println();
    }

    public static long fastexpo(long x, long y, long p) {
        long res = 1;
        while (y > 0) {
            if ((y & 1) == 1)
                res = ((res % p) * (x % p)) % p;
            y = y >> 1;
            x = ((x % p) * (x % p)) % p;
        }
        return res;
    }

    public static boolean[] sieve(int n) {
        boolean primes[] = new boolean[n + 1];
        Arrays.fill(primes, true);
        primes[0] = primes[1] = false;
        for (int i = 2; i * i <= n; i++) {
            if (primes[i]) {
                for (int j = i * i; j <= n; j += i)
                    primes[j] = false;
            }
        }
        return primes;
    }

    public static long gcd(long a, long b) {
        return (BigInteger.valueOf(a).gcd(BigInteger.valueOf(b))).longValue();
    }

    public static void merge(long a[], int l, int m, int r) {
        int n1, n2, i, j, k;
        n1 = m - l + 1;
        n2 = r - m;

        long L[] = new long[n1];
        long R[] = new long[n2];

        for (i = 0; i < n1; i++)
            L[i] = a[l + i];
        for (j = 0; j < n2; j++)
            R[j] = a[m + 1 + j];

        i = 0;
        j = 0;

        k = l;
        while (i < n1 && j < n2) {
            if (L[i] <= R[j]) {
                a[k] = L[i];
                i++;
            } else {
                a[k] = R[j];
                j++;
            }
            k++;
        }

        while (i < n1) {
            a[k] = L[i];
            i++;
            k++;
        }
        while (j < n2) {
            a[k] = R[j];
            j++;
            k++;
        }
    }

    public static void sort(long a[], int l, int r) {
        int m;
        if (l < r) {
            m = (l + r) / 2;
            sort(a, l, m);
            sort(a, m + 1, r);
            merge(a, l, m, r);
        }
    }
}