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.
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{

	public static void main (String[] args) throws Exception
	{
        InputStreamReader r = new InputStreamReader(System.in);
        BufferedReader sc = new BufferedReader(r);
        PrintWriter pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
 
        int n = Integer.parseInt(sc.readLine());
		String s=sc.readLine();
		String t=sc.readLine();
		int k=0;
		int i=0;
		int flag=0;
		StringBuffer s1=new StringBuffer("");
		StringBuffer s2=new StringBuffer(s);
		while(k<Math.pow(10,4) && i<n &&flag==0){
		    if(s2.charAt(i)!=t.charAt(i)){
		        
		       flag=1;
		        int index=-1;
		        //System.out.println(i+"ok");
		        for(int j=i+1;j<n;j++){
		            if(t.charAt(i)==s2.charAt(j)){
		                flag=0;
		                index=j;
		                //System.out.println(index+"ok");
		                break;
		            }
		        }
		        if(index!=-1){
		            for(int j=index;j>i;j--){
		                char temp=s2.charAt(j-1);
		                s2.setCharAt(j-1,s2.charAt(j));
		                s2.setCharAt(j,temp);		                
		                s1.append(j+" ");
		                ++k;
		            }
		        }
		    }
		    ++i;
		    
		}
		if(flag==1){
		    System.out.println("-1");
		}
		else if(k==0){
		    System.out.println("0");
		    System.out.println("");
		}
		else{
		    System.out.println(k);
		    System.out.println(s1.toString());
		}
		
	}
	}

