You are given two strings s and t, each of length n and consisting of lowercase Latin alphabets. You want to make s equal to t. 

You can perform the following operation on s any number of times to achieve it — 

  * Choose any substring of s and rotate it clockwise once, that is, if the selected substring is s[l,l+1...r], then it becomes s[r,l,l + 1 ... r - 1]. All the remaining characters of s stay in their position. 

For example, on rotating the substring [2,4] , string "abcde" becomes "adbce". 




A string a is a substring of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end.

Find the minimum number of operations required to convert s to t, or determine that it's impossible.

Input

The first line of the input contains a single integer t (1≤ t ≤ 2000) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer n (1≤ n ≤ 2000) — the length of the strings. 

The second and the third lines contain strings s and t respectively.

The sum of n over all the test cases does not exceed 2000.

Output

For each test case, output the minimum number of operations to convert s to t. If it is not possible to convert s to t, output -1 instead.

Example

Input


6
1
a
a
2
ab
ba
3
abc
cab
3
abc
cba
4
abab
baba
4
abcc
aabc


Output


0
1
1
2
1
-1

Note

For the 1-st test case, since s and t are equal, you don't need to apply any operation.

For the 2-nd test case, you only need to apply one operation on the entire string ab to convert it to ba.

For the 3-rd test case, you only need to apply one operation on the entire string abc to convert it to cab.

For the 4-th test case, you need to apply the operation twice: first on the entire string abc to convert it to cab and then on the substring of length 2 beginning at the second character to convert it to cba.

For the 5-th test case, you only need to apply one operation on the entire string abab to convert it to baba.

For the 6-th test case, it is not possible to convert string s to t.
import sys
N=sys.stdin.readline()
for T in range(int(N)):
    lenx=int(sys.stdin.readline())
    str1=sys.stdin.readline().strip()[:lenx]
    str2=sys.stdin.readline().strip()[:lenx]
    t={}
    f=True
    for one in str1:
        t[one]=t.get(one,0)+1
    for one in str2:
        t[one]=t.get(one,0)-1
        if t[one]<0:
            f=False
            break
    if not f:
        print -1
        continue
    cnt=0

    str1=str1[::-1]
    str2=str2[::-1]

    i=0
    q={}
    low={}
    for j  in range(lenx):
        x= str2[j]
        while  (q.get(x,0)==0) and (x!=str1[i]) :
            cnt+=1

            q[str1[i]]=q.get(str1[i],0)+1
            i+=1
        if (i<lenx) and (x==str1[i]) :
            low[j+1]=i+1
            i+=1
        else:
            low[j+1]=low[j]
            q[x]-=1
    low[0]=0
    max_value = 0
    dp = [[0 for j in xrange(0, lenx+1)] for i in xrange(0, lenx+1)]
    for i in xrange(1, lenx+1):
        for j in range(1, lenx+1):
            if (str2[i-1] == str1[j-1]) and ((dp[i-1][j-1]==i-1) or(  j>=low[i-1])) :
                dp[i][j] = dp[i-1][j-1] + 1
                max_value = max(max_value, dp[i][j])
            else:
                #if i==1:
                #    dp[i][j] =0
                #else:
                    dp[i][j] = max(dp[i][j-1], dp[i-1][j])
    print lenx-max_value
				     		  	   	   		 				 		