Note that the only difference between String Transformation 1 and String Transformation 2 is in the move Koa does. In this version the letter y Koa selects must be strictly greater alphabetically than x (read statement for better understanding). You can make hacks in these problems independently.

Koa the Koala has two strings A and B of the same length n (|A|=|B|=n) consisting of the first 20 lowercase English alphabet letters (ie. from a to t).

In one move Koa:

  1. selects some subset of positions p_1, p_2, …, p_k (k ≥ 1; 1 ≤ p_i ≤ n; p_i ≠ p_j if i ≠ j) of A such that A_{p_1} = A_{p_2} = … = A_{p_k} = x (ie. all letters on this positions are equal to some letter x).

  2. selects a letter y (from the first 20 lowercase letters in English alphabet) such that y>x (ie. letter y is strictly greater alphabetically than x).

  3. sets each letter in positions p_1, p_2, …, p_k to letter y. More formally: for each i (1 ≤ i ≤ k) Koa sets A_{p_i} = y.

Note that you can only modify letters in string A.




Koa wants to know the smallest number of moves she has to do to make strings equal to each other (A = B) or to determine that there is no way to make them equal. Help her!

Input

Each test contains multiple test cases. The first line contains t (1 ≤ t ≤ 10) — the number of test cases. Description of the test cases follows.

The first line of each test case contains one integer n (1 ≤ n ≤ 10^5) — the length of strings A and B.

The second line of each test case contains string A (|A|=n).

The third line of each test case contains string B (|B|=n).

Both strings consists of the first 20 lowercase English alphabet letters (ie. from a to t).

It is guaranteed that the sum of n over all test cases does not exceed 10^5.

Output

For each test case:

Print on a single line the smallest number of moves she has to do to make strings equal to each other (A = B) or -1 if there is no way to make them equal.

Example

Input


5
3
aab
bcc
4
cabc
abcb
3
abc
tsr
4
aabd
cccd
5
abcbd
bcdda


Output


2
-1
3
2
-1

Note

  * In the 1-st test case Koa: 
    1. selects positions 1 and 2 and sets A_1 = A_2 =  b (\color{red}{aa}b → \color{blue}{bb}b). 
    2. selects positions 2 and 3 and sets A_2 = A_3 =  c (b\color{red}{bb} → b\color{blue}{cc}). 

  * In the 2-nd test case Koa has no way to make string A equal B.

  * In the 3-rd test case Koa: 
    1. selects position 1 and sets A_1 =  t (\color{red}{a}bc → \color{blue}{t}bc). 
    2. selects position 2 and sets A_2 =  s (t\color{red}{b}c → t\color{blue}{s}c). 
    3. selects position 3 and sets A_3 =  r (ts\color{red}{c} → ts\color{blue}{r}). 
#   Author: yumtam
#   Created at: 2020-09-10 19:20

from __future__ import division, print_function
_interactive = False


def solve():
    n = input_as_list()
    a = [ord(c)-ord('a') for c in input()]
    b = [ord(c)-ord('a') for c in input()]

    tb = array_of(int, 20, 20)

    for ca, cb in zip(a, b):
        if ca > cb:
            print("-1")
            return
        if ca < cb:
            tb[ca][cb] = 1

    ans = 0
    for ca in range(20):
        ctb = tb[ca]
        if sum(ctb) > 0:
            least = ctb.index(1)
            for i in range(least+1, 20):
                tb[least][i] = tb[least][i] | ctb[i]
            ans += 1

    print(ans)


def main():
    for _ in range(int(input())):
        solve()


# Constants
INF = float('inf')
MOD = 10**9+7

# Python3 equivalent names
import os, sys, itertools
if sys.version_info[0] < 3:
    input = raw_input
    range = xrange

    filter = itertools.ifilter
    map = itertools.imap
    zip = itertools.izip

# print-flush in interactive problems
if _interactive:
    flush = sys.stdout.flush
    def printf(*args, **kwargs):
        print(*args, **kwargs)
        flush()

# Debug print, only works on local machine
LOCAL = "LOCAL_" in os.environ
debug_print = (print) if LOCAL else (lambda *x, **y: None)

# Fast IO
if (not LOCAL) and (not _interactive):
    from io import BytesIO
    from atexit import register
    sys.stdin = BytesIO(os.read(0, os.fstat(0).st_size))
    sys.stdout = BytesIO()
    register(lambda: os.write(1, sys.stdout.getvalue()))
    input = lambda: sys.stdin.readline().rstrip('\r\n')

# Some utility functions(Input, N-dimensional lists, ...)
def input_as_list():
    return [int(x) for x in input().split()]

def input_with_offset(o):
    return [int(x)+o for x in input().split()]

def input_as_matrix(n, m):
    return [input_as_list() for _ in range(n)]

def array_of(f, *dim):
    return [array_of(f, *dim[1:]) for _ in range(dim[0])] if dim else f()

# Start of external code templates...
# End of external code templates.

main()
