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.*;
import java.util.*;
public class HelloWorld{

     public static void main(String []args)throws IOException
     {
        //System.out.println("Hello World");
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        //StringTokenizer st=new StringTokenizer(br.readLine());
        int n=Integer.parseInt(br.readLine());
        char s[]=br.readLine().toCharArray();
        char t[]=br.readLine().toCharArray();
        ArrayList<Integer> ar=new ArrayList<Integer>();
       // System.out.println(ar.size());
        //int ar[]=new int[m+1];
        int c=0;int k=0;int check=0;int check1=0;
        for(int i=0;i<n;i++)
        {
            
            if(s[i]!=t[i])
            {
                if(ar.size()==0)k=0;
                else k=ar.size();
                check=0;int r=0; 
                for(int j=i+1;j<n;j++)
                {
                    if(s[j]==t[i])
                    {
                        c++;
                        ar.add(k,j);check=1;r=j;
                        break;
                    }
                    else
                    {
                        c++;
                        ar.add(k,j);
                    }
                }
                if(check==0){System.out.println(-1);check1=1;break;}
                for(int j=r;j>=i+1;j--)
                {
                    s[j]=s[j-1];
                }
                
            }
        }
        if(check1==0)
        {
            System.out.println(c);
            for(int j=0;j<ar.size();j++)
                {
                    System.out.print(ar.get(j)+" ");
                }
            
        }
        
     }
}