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.io.*;
import java.lang.reflect.Array;
import java.util.*;
import java.math.*;
import java.text.*;

import static java.lang.Math.*;
import static java.lang.System.*;

public class Solution {
    public static char flip(char ch) {
        if(ch == '0') return '1';
        return '0';
    }

    public static void main(String[] args) throws IOException {
        int T = cin.nextInt();
        for(int t = 0; t < T; t++) {
            int n = cin.nextInt();
            char[] a = cin.next().toCharArray();
            char[] b = cin.next().toCharArray();
            StringBuilder sb = new StringBuilder();
            int ct = 0;
            int ct1 = 0;
            for(int i = n - 1; i >= 1; i--) {
//                a[i] = ct1 % 2 == 0 ? a[i] : flip(a[i]);
                if(a[i] == b[i]) continue;
                // a[i] = flip(a[0]) a[0] = flip(a[i])
                char tmp = flip(a[0]);
                if(tmp != b[i]) {
                    sb.append(" ");
                    sb.append(1);
                    ct++;
                    a[0] = flip(a[0]);
//                    out.println(a);
                }
                sb.append(" ");
                sb.append(i + 1);
                ct++;
                ct1++;
                char[] tc = new char[n];
                for(int k = 0; k <= i; k++) {
                    tc[k] = flip(a[i - k]);
                }
                for(int k = 0; k <= i; k++) {
                    a[k] = tc[k];
                }
//                char tmp2 = a[0];
//                a[0] = flip(a[i]);
//                a[i] = flip(tmp2);
//                out.println(a);
            }
            if(a[0] != b[0]) {
                sb.append(" ");
                sb.append(1);
                ct++;
                a[0] = flip(a[0]);
            }
            String res = ct + sb.toString();
            out.println(res);
//            out.println(a);
        }
    }

    static String l2b(long[] nums) {
        String str1 = Long.toBinaryString(nums[1]);
        String res = String.format("%10s", str1);
        str1 = res.replaceAll("\\s", "0");
        String str2 = Long.toBinaryString(nums[0]);
        res = String.format("%10s", str2);
        str2 = res.replaceAll("\\s", "0");
        return str1 + str2;
    }

    private static void sort(double[] arr) {
        Double[] objArr = Arrays.stream(arr).boxed().toArray(Double[]::new);
        Arrays.sort(objArr);
        for (int i = 0; i < arr.length; i++) {
            arr[i] = objArr[i];
        }
    }

    private static void sort(int[] arr) {
        Integer[] objArr = Arrays.stream(arr).boxed().toArray(Integer[]::new);
        Arrays.sort(objArr);
        for (int i = 0; i < arr.length; i++) {
            arr[i] = objArr[i];
        }
    }

    private static void sort(long[] arr) {
        Long[] objArr = Arrays.stream(arr).boxed().toArray(Long[]::new);
        Arrays.sort(objArr);
        for (int i = 0; i < arr.length; i++) {
            arr[i] = objArr[i];
        }
    }
    // Fast IO v2
    static class FastScanner{
        BufferedReader br;
        StringTokenizer st;
        public FastScanner(InputStream in) {
            br = new BufferedReader(new InputStreamReader(in),16384);
            eat("");
        }
        public void eat(String s) {
            st = new StringTokenizer(s);
        }
        public String nextLine() {
            try {
                return br.readLine();
            } catch (IOException e) {
                return null;
            }
        }
        public boolean hasNext() {
            while(!st.hasMoreTokens()) {
                String s = nextLine();
                if(s==null) return false;
                eat(s);
            }
            return true;
        }
        public String next() {
            hasNext();
            return st.nextToken();
        }
        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong() {
            return Long.parseLong(next());
        }
        public double nextDouble() {
            return Double.parseDouble(next());
        }
    }

    static FastScanner cin = new FastScanner(System.in);

    static class ModMath {
        private static final int DEFAULT_MOD = 1_000_000_007;
        private final long mod;

        public ModMath(long mod, boolean unsafe) {
        /*if (!unsafe && !IntMath.isPrime(mod)) {
            throw new RuntimeException("This class is designed for primes!");
        }*/
            this.mod = mod;
        }

        public ModMath(long mod) {
            this(mod, false);
        }

        public ModMath() {
            this(DEFAULT_MOD, true);
        }

        public long mod(long x) {
            x %= mod;
            return x < 0 ? x + mod : x;
        }

        public long inv(long x) {
            //return pow(x, mod - 2);
            return mod(LongEuclidSolver.solve(x, mod).x);
        }

        public Factorial getFactorial(int n) {
            return new Factorial(this, n);
        }

    }

    static class Factorial {
        private final ModMath mod;
        private final long[] natural;
        private final long[] reverse;

        public Factorial(ModMath mod, int max) {
            this.mod = mod;
            this.natural = new long[max];
            this.reverse = new long[max];
            natural[0] = 1;
            for (int i = 1; i < max; i++) {
                natural[i] = mod.mod(natural[i - 1] * i);
            }
            reverse[max - 1] = mod.inv(natural[max - 1]);
            for (int i = max - 1; i > 0; i--) {
                reverse[i - 1] = mod.mod(reverse[i] * i);
            }
        }

        public long fact(long x) {
            return natural[(int) x];
        }

        public long factinv(long x) {
            return reverse[(int) x];
        }

        public long npr(long n, long r) {
            return n < r ? 0 : mod.mod(fact(n) * factinv(n - r));
        }

        public long ncr(long n, long r) {
            return mod.mod(npr(n, r) * factinv(r));
        }

        public String toString() {
            return "Factorial{" +
                    "natural=" + Arrays.toString(natural) +
                    ", reverse=" + Arrays.toString(reverse) +
                    '}';
        }

    }

    static class LongEuclidSolver {
        private LongEuclidSolver() {
        }

        public static Vec3l solve(long a, long b) {
            LongEuclidSolver.ReferenceLong p = new LongEuclidSolver.ReferenceLong(), q = new LongEuclidSolver.ReferenceLong();
            long d = solve(a, b, p, q);
            return new Vec3l(p.val, q.val, d);
        }

        private static long solve(long a, long b, LongEuclidSolver.ReferenceLong p, LongEuclidSolver.ReferenceLong q) {
            if (b == 0) {
                p.val = 1;
                q.val = 0;
                return a;
            } else {
                long d = solve(b, a % b, q, p);
                q.val -= (a / b) * p.val;
                return d;
            }
        }

        private static class ReferenceLong {
            private long val;

        }

    }

    static class Vec3l implements Comparable<Vec3l> {
        public long x;
        public long y;
        public long z;

        public Vec3l(long x, long y, long z) {
            this.x = x;
            this.y = y;
            this.z = z;
        }

        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Vec3i vec3i = (Vec3i) o;
            return x == vec3i.x &&
                    y == vec3i.y &&
                    z == vec3i.z;
        }

        public int hashCode() {
            return Objects.hash(x, y, z);
        }

        public String toString() {
            return "(" + x + ", " + y + ", " + z + ")";
        }

        public int compareTo(Vec3l o) {
            if (x == o.x) {
                if (y == o.y) {
                    return Long.compare(z, o.z);
                }
                return Long.compare(y, o.z);
            }
            return Long.compare(x, o.x);
        }

    }

    static class Vec3i implements Comparable<Vec3i> {
        public int x;
        public int y;
        public int z;

        public Vec3i(int x, int y, int z) {
            this.x = x;
            this.y = y;
            this.z = z;
        }

        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Vec3i vec3i = (Vec3i) o;
            return x == vec3i.x &&
                    y == vec3i.y &&
                    z == vec3i.z;
        }

        public int hashCode() {
            return Objects.hash(x, y, z);
        }

        public String toString() {
            return "(" + x + ", " + y + ", " + z + ")";
        }

        public int compareTo(Vec3i o) {
            if (x == o.x) {
                if (y == o.y) {
                    return Integer.compare(z, o.z);
                }
                return Integer.compare(y, o.z);
            }
            return Integer.compare(x, o.x);
        }

    }
}