Mr. Mime enjoys walking around town playing tricks on townspeople. In particular, Mr. Mime likes to trap unassuming individuals using invisible walls, forcing them to solve a puzzle for their freedom.
Today, Mr. Mime has trapped you and starts shuffling the air, throwing it at you until suddenly you're able to see a deck of cards being dealt out to a table in front of you! Looks like this deck of cards is your puzzle for the day. It seems to be a $$$52$$$ card deck with $$$4$$$ suits ($$$H$$$, $$$S$$$, $$$D$$$, $$$C$$$) and $$$13$$$ numbered cards for each suit (numbered $$$1$$$ through $$$13$$$). However, some cards are missing its suit, some cards are missing its number, and the rest are missing both. You see that there are $$$N$$$ cards that are missing its suit but not its number and $$$M$$$ cards that are missing its number but not its suit ($$$1 \leq N, M \lt 52$$$, $$$N + M \leq 52$$$). There isn't a single card that is complete with both a suit and number.
As you stare at these cards, Mr. Mime points at the deck and gives you a strange look. It seems that in order to be free, you must determine whether or not this deck is actually a valid $$$52$$$ card deck if you assign missing suits and numbers to all the cards. A valid $$$52$$$ card deck contains all $$$13$$$ unique numbers for each suit. Good luck solving Mr. Mime's puzzle!
The first line contains the number of test cases $$$t$$$ ($$$1 \leq t \leq 10^4$$$). The description of the test cases follow.
The first line of each test case consists of two integers $$$N$$$ and $$$M$$$ ($$$1 \leq N, M \lt 52$$$, $$$N + M \leq 52$$$), the number of cards that are either missing its suit or number but not both, respectively.
The second line of each test case consists of $$$N$$$ space-separated integers, providing the number of a card that doesn't have its suit (from $$$1$$$ to $$$13$$$).
The third line of each test case consists of $$$M$$$ space-separated characters, providing the suit of a card that doesn't have its number (either $$$H$$$, $$$S$$$, $$$D$$$, or $$$C$$$).
For each test case, output "YES" if the cards provided are a valid deck. Otherwise, output "NO". You can output the answer in any case (for example, the strings "yEs", "yes", "Yes" and "YES" will be recognized as a positive answer).
53 41 2 3H S D C5 21 1 1 1 1S D12 121 1 1 1 2 2 2 2 3 4 5 6H H H H H H H H H H H H12 111 1 1 1 2 2 2 2 3 4 5 6H H H H H H H H H H H17 191 1 1 2 2 3 3 3 3 4 4 4 4 5 5 5 5H H H H H H H H H S S S S S S S S S H
YES NO NO YES YES
In the first test case, a possible assignment of the cards is $$$(1, H)$$$, $$$(2, H)$$$, $$$(3, H)$$$ for the cards that don't have its suit and $$$(5, H), (6, S), (7, D), (8, C)$$$ for the cards that don't have its number. The remaining cards (missing both suit and number) can be assigned to fill up the remaining $$$45$$$ cards to form a valid deck.
In the second test case, it's not possible for there to be $$$5$$$ cards that have number $$$1$$$. There can only be $$$4$$$ cards with the same number for each suit, so it is not possible to form a valid deck.
