Flipper#1189

Flipper

1 second

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Medium

Little Bobby Roberts (son of Big Bob, of Problem G) plays this solitaire memory game called Flipper. He starts with $n$ cards, numbered $1$ through $n$ , and lays them out in a row with the cards in order left-to-right. (Card $1$ is on the far left; card $n$ is on the far right.) Some cards are face up and some are face down. Bobby then performs $n - 1$ n - 1 flips — either right flips or left flips.

In a right flip, he takes the pile to the far right and flips it over onto the card to its immediate left. For example, if the rightmost pile has cards $A$ , $B$ , $C$ (from top to bottom) and card $D$ is to the immediate left, then flipping the pile over onto card $D$ would result in a pile of $4$ cards: $C$ , $B$ , $A$ , $D$ (from top to bottom). A left flip is analogous.

After the very last flip, there will be a single pile of cards — some face up, some face down. For example, suppose Bobby deals out $5$ cards (numbered $1$ through $5$ ) with cards $1$ through $3$ initially face up and cards $4$ and $5$ initially face down. If Bobby performs $2$ right flips, then $2$ left flips, the pile will be (from top to bottom) a face down $2$ , a face up $1$ , a face up $4$ , a face down $5$ , and a face up $3$ .

Now Bobby is very sharp and you can ask him what card is in any position and he can tell you! You will write a program that matches Bobby’s amazing feat.

Input

Each test case consists of $4$ lines. The first line contains a positive integer $n$ ( $2 \leq n \leq 100$ 2 \leq n \leq 100) — the number of cards laid out. The second line is a string of $n$ characters. Character $U$ indicates the corresponding card is dealt face up and character $D$ indicates the card is face down. The third line is a string of $n - 1$ n - 1 characters showing the order of flips Bobby performs. Each character is either $R$ (right flip) or $L$ (left flip). The fourth line is of the form $m q_{1} q_{2} \dots q_{m}$ m\ q_1\ q_2\ \ldots\ q_m, where $m$ is a positive integer and $1 \leq q_{i} \leq n$ 1 \leq q_i \leq n. Each $q_{i}$ q_i is a query for the card's position in the pile ( $1$ is the top card, $n$ is the bottom card). A line containing $0$ indicates end of input.

Output

For each test case, output $m + 1$ m + 1 lines. The first line should be:

Pile $t$

where $t$ is the test case number (starting at $1$ ). Each of the next $m$ lines should be

Card $q_{i}$ q_i is a face up $k$ .

Card $q_{i}$ q_i is a face down $k$ .

accordingly, for $i = 1, \dots, m$ i = 1, \ldots, m, where $k$ is the card number.

For example, in the $5$ card example above, if $q_{i} = 3$ q_i = 3, then the answer would be

Card 3 is a face up 4.

Examples

Example 1