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.
num_of_smvl=input()
first_str=str(input())
second_str=str(input())
if first_str == second_str:
    print('0')
    exit()
ar1=[]
ar2=[]
ar3=[]
indexs=int
i=0    
while i<len(first_str):
    ar1.append(first_str[i])
    ar2.append(second_str[i])
    i+=1
for el in ar1:
    if ar1.count(el)==ar2.count(el):
        continue
    else:
        print('-1')
        exit()

j=0        
i=0
while i<int(num_of_smvl):
    if first_str[i]==second_str[i]:
        #print('ok')
        #print(first_str[i])
        #print( second_str[i])
        i+=1
    else:
        indexs=first_str.index(second_str[i],i,int(num_of_smvl))
        #print('index '+str(indexs))
        if indexs+1<int(num_of_smvl):
            first_str=first_str[:i]+first_str[indexs]+first_str[i:indexs]+first_str[indexs+1:]
            #print(first_str)
            j=i
            while indexs>j:
                ar3.append(indexs)
                indexs=indexs-1
            i+=1
        else:
            first_str=first_str[:i]+first_str[indexs]+first_str[i:indexs]
            #print(first_str)
            j=i
            while indexs>j:
                ar3.append(indexs)
                indexs=indexs-1
            i+=1
print(len(ar3))
print(str(ar3).replace(',',' ')[1:-1])