Third Group Exam

One teacher came up with a new format for an exam. The exam consists of $n$ blocks, one for each topic. A student receives a grade $c_i$ for the $i$-th block, for every $i$ from $1$ to $n$, and all grades are independent. Each grade is an integer from $0$ to $100$, inclusive.

For each block, a student chooses one way to earn the grade: answer a theoretical question or solve a practical problem. The exam is passed successfully if at least $a$ blocks were graded by answering a theoretical question and at least $b$ blocks were graded by solving a practical problem. If the exam is passed, the final grade $C$ is the sum of the grades for all blocks: $C = \sum_{i=1}^n c_i$.

Ilya is about to take the exam. For block $i$, answering the theoretical question gives him a grade of $x_i$, and solving the practical problem gives him a grade of $y_i$. Help him decide which blocks (at least $a$ of them) he should answer by theory and which blocks (at least $b$ of them) he should solve by practice, so that his total exam score is as large as possible.

The first line contains three integers $n$, $a$ and $b$, the total number of topics, the minimum number of blocks to pass by theory, and the minimum number of blocks to pass by practice ($1 \le n \le 2 \cdot 10^5$; $0 \le a, b \le n$). It is guaranteed that $a + b \le n$.

The second line contains $n$ integers $x_i$, the grades for answering the theoretical questions ($0 \le x_i \le 100$).

The third line contains $n$ integers $y_i$, the grades for solving the practical problems ($0 \le y_i \le 100$).

The first line must contain a single integer $C$, the maximum total grade Ilya can get.

The second line must contain $n$ space-separated characters, where the $i$-th character is T if Ilya should answer the theoretical question for block $i$, and P if he should solve the practical problem. At least $a$ characters must be T, and at least $b$ characters must be P.