CF1703C Cypher

Luca has a cypher made up of a sequence of $ n $ wheels, each with a digit $ a_i $ written on it. On the $ i $ -th wheel, he made $ b_i $ moves. Each move is one of two types: - up move (denoted by $ \texttt{U} $ ): it increases the $ i $ -th digit by $ 1 $ . After applying the up move on $ 9 $ , it becomes $ 0 $ . - down move (denoted by $ \texttt{D} $ ): it decreases the $ i $ -th digit by $ 1 $ . After applying the down move on $ 0 $ , it becomes $ 9 $ . Example for $ n=4 $ . The current sequence is 0 0 0 0.Luca knows the final sequence of wheels and the moves for each wheel. Help him find the original sequence and crack the cypher.

The first line contains a single integer $ t $ ( $ 1 \leq t \leq 100 $ ) — the number of test cases. The first line of each test case contains a single integer $ n $ ( $ 1 \leq n \leq 100 $ ) — the number of wheels. The second line contains $ n $ integers $ a_i $ ( $ 0 \leq a_i \leq 9 $ ) — the digit shown on the $ i $ -th wheel after all moves have been performed. Then $ n $ lines follow, the $ i $ -th of which contains the integer $ b_i $ ( $ 1 \leq b_i \leq 10 $ ) and $ b_i $ characters that are either $ \texttt{U} $ or $ \texttt{D} $ — the number of moves performed on the $ i $ -th wheel, and the moves performed. $ \texttt{U} $ and $ \texttt{D} $ represent an up move and a down move respectively.

For each test case, output $ n $ space-separated digits — the initial sequence of the cypher.

In the first test case, we can prove that initial sequence was $ [2,1,1] $ . In that case, the following moves were performed: - On the first wheel: $ 2 \xrightarrow[\texttt{D}]{} 1 \xrightarrow[\texttt{D}]{} 0 \xrightarrow[\texttt{D}]{} 9 $ . - On the second wheel: $ 1 \xrightarrow[\texttt{U}]{} 2 \xrightarrow[\texttt{D}]{} 1 \xrightarrow[\texttt{U}]{} 2 \xrightarrow[\texttt{U}]{} 3 $ . - On the third wheel: $ 1 \xrightarrow[\texttt{D}]{} 0 \xrightarrow[\texttt{U}]{} 1 $ . The final sequence was $ [9,3,1] $ , which matches the input.