You are given two strings s and t. Both strings have length n and consist of lowercase Latin letters. The characters in the strings are numbered from 1 to n.

You can successively perform the following move any number of times (possibly, zero):

  * swap any two adjacent (neighboring) characters of s (i.e. for any i = \{1, 2, ..., n - 1\} you can swap s_i and s_{i + 1}). 



You can't apply a move to the string t. The moves are applied to the string s one after another.

Your task is to obtain the string t from the string s. Find any way to do it with at most 10^4 such moves.

You do not have to minimize the number of moves, just find any sequence of moves of length 10^4 or less to transform s into t.

Input

The first line of the input contains one integer n (1 ≤ n ≤ 50) — the length of strings s and t.

The second line of the input contains the string s consisting of n lowercase Latin letters.

The third line of the input contains the string t consisting of n lowercase Latin letters.

Output

If it is impossible to obtain the string t using moves, print "-1".

Otherwise in the first line print one integer k — the number of moves to transform s to t. Note that k must be an integer number between 0 and 10^4 inclusive.

In the second line print k integers c_j (1 ≤ c_j < n), where c_j means that on the j-th move you swap characters s_{c_j} and s_{c_j + 1}.

If you do not need to apply any moves, print a single integer 0 in the first line and either leave the second line empty or do not print it at all.

Examples

Input

6
abcdef
abdfec


Output

4
3 5 4 5 


Input

4
abcd
accd


Output

-1

Note

In the first example the string s changes as follows: "abcdef" → "abdcef" → "abdcfe" → "abdfce" → "abdfec".

In the second example there is no way to transform the string s into the string t through any allowed moves.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        BObtainingTheString solver = new BObtainingTheString();
        solver.solve(1, in, out);
        out.close();
    }

    static class BObtainingTheString {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.ni();
            StringBuilder s = new StringBuilder(in.n());
            String t = in.n();
            int[] countS = new int[26];
            int[] countT = new int[26];
            for (int i = 0; i < n; ++i) {
                ++countS[s.charAt(i) - 'a'];
                ++countT[t.charAt(i) - 'a'];
            }
            boolean possible = true;
            for (int i = 0; i < 26; ++i) {
                if (countS[i] != countT[i]) {
                    possible = false;
                    break;
                }
            }
            if (!possible) {
                out.println(-1);
                return;
            }
            int moves = 0;
            ArrayList<Integer> al = new ArrayList<>();
            for (int i = 0; i < n; ++i) {
                int indexT = i;
                while (s.charAt(indexT) != t.charAt(i))
                    ++indexT;
                for (int j = indexT - 1; j >= i; --j) {
                    al.add(j + 1);
                    char temp = s.charAt(j);
                    s.setCharAt(j, s.charAt(j + 1));
                    s.setCharAt(j + 1, temp);
                }
                moves += (indexT - i);
            }
            out.println(moves);
            for (int a : al)
                out.print(a + " ");
            out.println();
        }

    }

    static class InputReader {
        BufferedReader br;
        StringTokenizer st;

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

        public InputReader(InputStream inputStream) {
            br = new BufferedReader(new InputStreamReader(inputStream));
        }

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

        public int ni() {
            return Integer.parseInt(n());
        }

    }
}

