Calendar of Events

Marketing people are very creative and attend a great many meetings. The company's monthly schedule lists one meeting for each of the first $N$ days of the month. Every meeting is identified by a non-negative integer, and the same identifier may appear on several days.

The current schedule (the old order) must be turned into a chosen new order. The only operation the planning department may perform is a request: pick a number $D$ and reverse the meetings of the first $D$ days. For example, if the current order is 1 2 3 4 5, a request with $D = 3$ turns it into 3 2 1 4 5.

Because an identifier may repeat, occurrences are matched by order: if a value is the $k$-th occurrence from the left in the old order, that meeting must reach the position of the $k$-th occurrence of the same value in the new order. This assigns to every day of the old schedule a unique target position in $1 \ldots N$.

The department always follows this fixed procedure. For $\text{size} = N, N-1, \ldots, 2$ in this order:

• Let $p$ be the current position (counting from the front) of the day whose target position is $\text{size}$; this day is always among the first $\text{size}$ days.
• If $p = \text{size}$, issue no request.
• Otherwise, if $p \neq 1$, first issue the request $p$ (reverse the first $p$ days); then issue the request $\text{size}$ (reverse the first $\text{size}$ days).

Report every request the procedure issues, in order.

The input contains several reorganizations; the last one is followed by a line containing a single zero.

Each reorganization consists of three lines. The first line is an integer $N$ ($1 \le N \le 30$), the number of days considered. The second line is the old schedule and the third line is the new schedule; each lists $N$ meeting identifiers (non-negative integers) separated by spaces. Both schedules contain the same multiset of identifiers, and some may appear more than once.

For each reorganization, print one line with the request numbers $D_1\ D_2\ \ldots\ D_k$ issued by the procedure, separated by single spaces ($1 \le D_i \le N$). If the old and new schedules are already equal, the procedure issues no request; print an empty line.