A15217. 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.