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 org.omg.CORBA.INTERNAL;
import sun.rmi.runtime.Log;

import java.io. *;
import java.util.*;
import static java.lang.Math.*;
public class Main {

    static final FastReader sc = new FastReader(System.in);
    static final PrintWriter pw = new PrintWriter(System.out);

    static int visited[];
    static ArrayList<ArrayList<Integer>> adjlist;
    static class edge implements  Comparator<edge>{
        int dest;
        int cost;

        public edge(int dest, int cost) {
            this.dest = dest;
            this.cost = cost;
        }

        @Override
        public int compare(edge o1, edge o2) {
            return o1.cost-o2.cost;
        }
    }

    static int dist[];
    static int nodesinSubtree[];
    static int color[];
    static ArrayList<Integer> res1;
    static ArrayList<Integer> res2;

    static class Graph{
        int V;
        ArrayList<ArrayList<edge>> adj;
        PriorityQueue<edge> pq;

        public Graph(int V){
            this.V = V;
            adj = new ArrayList<>(V);
            pq = new PriorityQueue<>(V,new edge(-1,-1));
            dist = new int[V];
            nodesinSubtree = new int[V];
            color = new int[V];
            Arrays.fill(color,-1);
            for(int i=0; i<V; i++){
                dist[i] = Integer.MAX_VALUE;
                adj.add(i,new ArrayList<>());
            }
        }

        void addedge(int u, int v, int w ){
            adj.get(u).add(new edge(v,w));
            //adj.get(v).add(new edge(u,w));
        }

        void rDfs(int src, int e){
            //nodes in a subtree
            nodesinSubtree[src] = 1;
            for(int i=0; i<adj.get(src).size(); i++){
                if(adj.get(src).get(i).dest==e){
                    continue;
                }
                rDfs(adj.get(src).get(i).dest,src);
                nodesinSubtree[src]+=nodesinSubtree[adj.get(src).get(i).dest];
            }
        }




        void uBFS(int src){
            Queue<edge> q = new LinkedList<>();
            color = new int[V];
            q.add(new edge(src,0));
            color[src] = 0;
            while (!q.isEmpty()){
                int u = q.poll().dest;
                for(int i=0; i<adj.get(u).size(); i++){
                    if(color[adj.get(u).get(i).dest]==color[u]){
                        color[adj.get(u).get(i).dest] = color[u]+1;
                        q.add(new edge(adj.get(u).get(i).dest,0));
                    }
                }
            }
        }



        int DFS(int src){
            Stack<edge> st = new Stack<>();
            boolean visited[] = new boolean[V];
            visited[src] = true;
            st.push(new edge(src,0));
            dist[src] = 0;
            color[src] = 1;
            while (!st.empty()){
                int u = st.peek().dest;
                st.pop();
                for(int i=0; i<adj.get(u).size(); i++){
                    if(color[adj.get(u).get(i).dest]==0) {
                        if (color[u] == 0) {
                            color[adj.get(u).get(i).dest] = 1;
                        } else {
                            color[adj.get(u).get(i).dest] = 0;
                        }
                        st.push(new edge(adj.get(u).get(i).dest,0));
                    }else{
                        if(color[u]==0 && color[adj.get(u).get(i).dest]==0){
                            return -1;
                        }
                        if(color[u]==1 && color[adj.get(u).get(i).dest]==1){
                            return -1;
                        }
                    }
                }
            }
            return 0;
        }
    }


/*
        void dijkstra(int src){
            for(int i=0; i<V; i++){
                dist[i] = Integer.MAX_VALUE;
            }
            dist[src] = 0;
            pq.add(new edge(src,0));
            while (!pq.isEmpty()){
                int u = pq.poll().dest;
                for(int i=0; i<adj.get(u).size(); i++){
                    int v = adj.get(u).get(i).dest;
                    int w = adj.get(u).get(i).cost;
                    if(dist[u]+w<=dist[v]){
                        dist[v] = dist[u] + w;
                        pq.add(new edge(v,dist[v]));
                    }
                }
            }

        }


    }

 */



    static  int I[];
    static  int  L[];
    static void LIS(int n, int arr[]){
        I = new int[n+1];
        L = new int[n];
        I[0] = Integer.MIN_VALUE;
        for(int i=1;i<=n; i++){
            I[i] = Integer.MAX_VALUE;
        }

        int lisLength = 1;

        for(int i=n-1; i>=0; i--) {
            int low = 1;
            int high = lisLength;
            int mid = 0;
            while (low < high) {
                mid = (low + high) >> 1;
                if (I[mid] <= arr[i]) {
                    high = mid;
                } else {
                    low = mid + 1;
                }
            }

            I[high] = arr[i];
            L[i] = high;
            if(lisLength<=high){
                lisLength++;
            }
        }
    }

    public static long gcd(long a, long b)
    {
        if (a == 0)
            return b;

        return gcd(b%a, a);
    }

    public static long lcm(long a, long b)
    {
        return (a*b)/gcd(a, b);
    }

    static long nCr(long n, long r)
    {
        return fact(n) / (fact(r) * fact(n - r));
    }

    // Returns factorial of n
    static long fact(long n)
    {
        long res = 1;
        for (int i = 2; i <= n; i++)
            res = (res * i)%MOD;
        return res;
    }


    static int MOD = 1000000007;
    static int power(int x, int y, int p)
    {

        // Initialize result
        int res = 1;

        // Update x if it is more than or
        // equal to p
        x = x % p;

        while (y > 0)
        {

            // If y is odd, multiply x
            // with result
            if (y % 2 == 1)
                res = (res * x) % p;

            // y must be even now
            y = y >> 1; // y = y/2
            x = (x * x) % p;
        }

        return res;
    }

    // Returns n^(-1) mod p
    static int modInverse(int n, int p)
    {
        return power(n, p-2, p);
    }

    static int nCrModPFermat(int n, int r,
                             int p)
    {

        if (r == 0)
            return 1;


        int[] fac = new int[n+1];
        fac[0] = 1;

        for (int i = 1 ;i <= n; i++)
            fac[i] = fac[i-1] * i % p;

        return (fac[n]* modInverse(fac[r], p)
                % p * modInverse(fac[n-r], p)
                % p) % p;
    }

    static int[] phi;

    static void generatePhi(int n){
        phi = new int[n+1];

        for(int i = 0; i<=n; i++){
            phi[i] = i;
        }

        for(int i=2; i<=n; i++){
            if(phi[i]==i){
                for(int j= i; j<=n; j+=i){
                    phi[j] -= (phi[j]/i);
                }
            }
        }
    }

    static int gcdCount(int n, int d){
        return phi[n/d];
    }

    static boolean prime[];
    static int smallestFactor[];

    static void sieveOfEratosthenes(int n)
    {
        prime = new boolean[n+1];
        smallestFactor = new int[n+1];

        smallestFactor[1] = 1;
        for(int i=2;i<n;i++) {
            prime[i] = true;
            smallestFactor[i] = i;
        }

        for(int p = 2; p*p <=n; p++)
        {
            if(prime[p])
            {
                smallestFactor[p] = p;
                for(int i = p*p; i <= n; i += p) {
                    prime[i] = false;
                    smallestFactor[i] = min(p,smallestFactor[i]);
                }
            }
        }

    }

    static double Logx(double n, int x){
        return log(n)/log(x);
    }

    static boolean isPrime(long n){
        if(n<2){
            return false;
        }
        for(int i = 2; i*i<=n; i++){
            if(n%i==0){
                return false;
            }
        }
        return true;
    }

    static int sumOfDigits(int n){
        int digitSum = 0;
        while (n>0){
            digitSum+=n%10;
            n/=10;
        }
        return digitSum;
    }

    static int a[];
    static int c[];


    static void PrefixFlip(int l){
        c = new int[l];
        for(int i =0; i<l; i++){
            if(a[i]==0){
                a[i]=1;
            }else{
                a[i]=0;
            }
        }
        for(int i =0; i<l; i++){
            c[i] = a[l-i-1];
        }
        for(int i =0; i<l; i++){
            a[i] = c[i];
        }

    }



    public static void main(String[] args) {

        int testcase = sc.nextInt();

        while (testcase-->0) {
            int n = sc.nextInt();
            a = new int[n];
            int b[] = new int[n];
            for(int i =0; i<n; i++){
                a[i] = sc.nextChar()-'0';
            }

            for(int i = 0; i<n; i++){
                b[i] = sc.nextChar()-'0';
            }

            int k = 0;

            int end = n-1;
            int start = 0;
            int endb = n-1;
            int flip = 0;

            ArrayList<Integer> res = new ArrayList<>();
            int number = 0;
            int firstnumber = 0;

            while (endb>=0){

                if(flip%2==0){
                    number = a[end];
                    if(number!=b[endb]){
                        firstnumber = a[start];
                        start++;
                        if(firstnumber==b[endb]){
                            k+=2;
                            res.add(1);
                            res.add(endb+1);
                            flip++;
                        }else{
                            k+=1;
                            res.add(endb+1);
                            flip++;
                        }
                    }else{
                        end--;
                    }

                }else{
                    if(a[start]==0){
                        number = 1;
                    }else{
                        number = 0;
                    }

                    if(number!=b[endb]){
                        if(a[end]==0){
                            firstnumber = 1;
                        }else{
                            firstnumber = 0;
                        }
                        end--;
                        if(firstnumber==b[endb]){
                            k+=2;
                            res.add(1);
                            res.add(endb+1);
                            flip++;
                        }else{
                            k+=1;
                            res.add(endb+1);
                            flip++;
                        }
                    }else{
                        start++;
                    }
                }

                endb--;

            }

            if(k!=0) {
                pw.print(k + " ");
            }else{
                pw.println(k);
            }
            for(int i =0 ;i<k; i++){
                if(i!=k-1){
                    pw.print(res.get(i)+" ");
                }else{
                    pw.println(res.get(i));
                }
            }


        }


        pw.flush();

    }

    static void debug(Object...obj) {
        System.err.println(Arrays.deepToString(obj));
    }

    static class FastReader {
        InputStream is;
        private byte[] inbuf = new byte[1024];
        private int lenbuf = 0, ptrbuf = 0;

        public FastReader(InputStream is) {
            this.is = is;
        }

        public int readByte(){
            if(lenbuf == -1)throw new InputMismatchException();
            if(ptrbuf >= lenbuf){
                ptrbuf = 0;
                try {
                    lenbuf = is.read(inbuf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if(lenbuf <= 0)
                    return -1;
            }
            return inbuf[ptrbuf++];
        }
        public boolean isSpaceChar(int c) {
            return !(c >= 33 && c <= 126);
        }
        public int skip() {
            int b;
            while ((b = readByte()) != -1 && isSpaceChar(b)) ;
            return b;
        }
        public String next(){
            int b = skip();
            StringBuilder sb = new StringBuilder();
            while(!(isSpaceChar(b))) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }
        public String nextLine(){
            int b = readByte();
            StringBuilder sb = new StringBuilder();
            while(b != '\n' || b != '\r'){
                sb.appendCodePoint(b);
            }
            return sb.toString();
        }
        public int nextInt() {
            int num = 0, b;
            boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
            if (b == '-') {
                minus = true;
                b = readByte();
            }
            while (true) {
                if (b >= '0' && b <= '9') {
                    num = (num << 3) + (num << 1) + (b - '0');
                } else {
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }
        public long nextLong() {
            long num = 0;
            int b;
            boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
            if (b == '-') {
                minus = true;
                b = readByte();
            }
            while (true) {
                if (b >= '0' && b <= '9') {
                    num = (num << 3) + (num << 1) + (b - '0');
                } else {
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }
        public double nextDouble() {
            return Double.parseDouble(next());
        }
        public char[] next(int n){
            char[] buf = new char[n];
            int b = skip(), p = 0;
            while (p < n && !(isSpaceChar(b))) {
                buf[p++] = (char) b;
                b = readByte();
            }
            return n == p ? buf : Arrays.copyOf(buf, p);
        }
        public char nextChar () {
            return (char) skip();
        }
    }
}