String Transformation 1

题意翻译

有字符串$A$，$B$，每次在$A$中选取若干个**相同**的字母（设为$x$），改成另一个字母(设为$y$)，需要满足$x<y$，问将A改成B的最少操作。 数据范围： 组数t$1 \le t \le 10$ 字符串长度n $1 \le n \le 10^5$，保证$A$，$B$长度相等，且所有组数长度不超过$10^5$

题目描述

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, \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 $ ). 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, \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!

输入输出格式

输入格式

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 $ .

输出格式

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.

输入输出样例

输入样例 #1

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

输出样例 #1

2
-1
3
2
-1

说明

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