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:

  selects some subset of positions $p_1, p_2, \ldots, p_k$ ($k \ge 1; 1 \le p_i \le n; p_i \neq p_j$ if $i \neq j$) of $A$ such that $A_{p_1} = A_{p_2} = \ldots = A_{p_k} = x$ (ie. all letters on this positions are equal to some letter $x$).

  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 $x$).

  sets each letter in positions $p_1, p_2, \ldots, p_k$ to letter $y$. More formally: for each $i$ ($1 \le i \le k$) 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 $t$ ($1 \le t \le 10$) — the number of test cases. Description of the test cases follows.

The first line of each test case contains one integer $n$ ($1 \le n \le 10^5$) — 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:   selects positions $1$ and $2$ and sets $A_1 = A_2 = $ b ($\color{red}{aa}b \rightarrow \color{blue}{bb}b$).  selects positions $2$ and $3$ and sets $A_2 = A_3 = $ c ($b\color{red}{bb} \rightarrow b\color{blue}{cc}$). 

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

  In the $3$-rd test case Koa:   selects position $1$ and sets $A_1 = $ t ($\color{red}{a}bc \rightarrow \color{blue}{t}bc$).  selects position $2$ and sets $A_2 = $ s ($t\color{red}{b}c \rightarrow t\color{blue}{s}c$).  selects position $3$ and sets $A_3 = $ r ($ts\color{red}{c} \rightarrow ts\color{blue}{r}$).

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'import sys\ninput = sys.stdin.readline\n\nt=int(input())\nfor tests in range(t):\n    n=int(input())\n    A=input().strip()\n    B=input().strip()\n\n    for i in range(n):\n        if A[i]>B[i]:\n            print(-1)\n            break\n    else:\n        DICT=dict()\n\n        for i in range(n):\n            a=A[i]\n            b=B[i]\n\n            if a==b:\n                continue\n\n            if a in DICT:\n                DICT[a].add(b)\n            else:\n                DICT[a]={b}\n\n        #print(DICT)\n\n        ANS=0\n\n        for x in "abcdefghijklmnopqrst":\n            if x in DICT and DICT[x]!=set():\n                ANS+=1\n                MIN=min(DICT[x])\n                if MIN in DICT:\n                    DICT[MIN]=DICT[MIN]|DICT[x]-{MIN}\n                else:\n                    DICT[MIN]=DICT[x]-{MIN}\n        print(ANS)\n            \n\n    \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13523