11B. Prison Watch

There are $n$ prison cells in a row, numbered from $1$ to $n$.

There is one guard in each cell. The direction of the guards is given by a string $s$ of length $n$.

• If $s_i = L$, then guard $i$ sees every cell $j$ such that $1 \le j \le i$.
• If $s_i = R$, then guard $i$ sees every cell $j$ such that $i \le j \le n$.

In particular, every guard sees their own cell.

Hiring guard $i$ costs $a_i$.

For each test case, find the minimum total cost needed to hire some guards so that every cell is seen by at least one hired guard.