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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

public class Main {
    public static void main(String[] args) {
        FastReader sc = new FastReader();
        int tt = sc.nextInt();
        while (tt-- > 0) {
            int n = sc.nextInt();
            String aStr = sc.nextLine();
            char []arr = aStr.toCharArray();
            String bStr = sc.nextLine();
            char []brr = bStr.toCharArray();

            DblLinkedList dll = build(arr);

            List<Integer> ans = new ArrayList<>();

            boolean toggled = false;
            boolean zeroToggled = false;
            Node currNode = dll.end;

            for(int i = n - 1; i >= 0 && currNode != null; --i){
                //print(dll);
                //System.out.println("currNode : " + currNode);
                if((currNode.val == brr[i] && !toggled)
                            || (currNode.val != brr[i] && toggled)){

                    if(!toggled)
                        currNode = currNode.prev;
                    else
                        currNode = currNode.next;

                    continue;
                }

                if ((dll.start.val == brr[i] && !toggled)
                        || ((dll.start.val != brr[i] && toggled))) {
                    ans.add(1);
                    //zeroToggled = !zeroToggled;
                    //toggleAndRev(dll, dll.start, toggled);
                }
                ans.add(i + 1);
                currNode = toggleAndRev(dll, currNode, toggled);
                toggled = !toggled;
                //System.out.println(ans);
            }

            System.out.print(ans.size() +" ");
            for(int p : ans)
                System.out.print(p +" ");
            System.out.println();

        }
    }

    static void print(DblLinkedList dll){
        System.out.println("--print--");
        Node node = dll.start;
        while(node != null){
            System.out.print(node +", ");
            node = node.next;
        }
        System.out.println("------");
    }

    private static Node toggleAndRev(DblLinkedList dll, Node right, boolean toggled){
        //System.out.println("right : " + right);
        if(right == dll.start){
           /* if(dll.start.val == '1')
                dll.start.val = '0';
            else
                dll.start.val = '1';*/
            return null;
        }
        else{
            Node nextNode;
            if(toggled){
/*                Node rem = right.next;
                dll.start.prev = rem;
                if(rem != null)
                    rem.prev = dll.start;*/
                //System.out.println("Toggled");
                nextNode = dll.start.prev;

                dll.start.prev.next = null;
                dll.start.prev = null;

                /*right.prev.next = null;
                right.prev = null;*/
            }
            else{
/*                Node rem = right.prev;
                dll.start.next = rem;
                if(rem != null)
                    rem.next = dll.start;*/
                //System.out.println("Not Toggled");
                nextNode = dll.start.next;

                dll.start.next.prev = null;
                dll.start.next = null;

                /*right.next.prev = null;
                right.next = null;*/

            }
            dll.start = right;
            //System.out.println("return " + nextNode);
            return  nextNode;
        }
    }

    private static DblLinkedList build(char []arr){
        int n = arr.length;
        if(n == 0)
            return null;
        Node start = new Node(arr[0]);
        Node end = start;
        for(int i = 1; i < n; ++i){
            Node node = new Node(arr[i]);
            node.prev = end;
            end.next = node;
            end = node;
            node.id = i;
        }

        DblLinkedList dll = new DblLinkedList(start, end);
        return dll;
    }

    private static class DblLinkedList{
        Node start;
        Node end;

        public DblLinkedList(Node start, Node end) {
            this.start = start;
            this.end = end;
        }
    }
    private static class Node{
        int id;
        char val;
        Node prev, next;
        Node(char val){
            this.val = val;
        }


        @Override
        public String toString() {
            return " { " + id +
                    " val=" + val +
                    '}';
        }
    }

    private static class FastReader {
        private BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        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;
        }
    }


}