5C. Permutation from Direction String

Consider any permutation $p_1, p_2, \dots, p_n$ of the integers $1, 2, \dots, n$.
Define $p_0 = n+1$ and $p_{n+1} = n+2$.

For each index $i$ ($1 \le i \le n$) we compute a character $c_i$ as follows:

• Let $x$ be the index of the nearest greater element to the left of $i$: $x = \max\{j \mid 0 \le j < i \text{ and } p_j > p_i\}$.
• Let $y$ be the index of the nearest greater element to the right of $i$: $y = \min\{j \mid i < j \le n+1 \text{ and } p_j > p_i\}$.
• If $p_x < p_y$ then $c_i =$ L, otherwise $c_i$ = R.

In other words, we look at the closest larger element on the left and the closest larger element on the right. The character L means the left one is smaller, R means the right one is smaller.

Now you are given the string $s$. Determine whether there exists a permutation $p$ such that $c_i = s_i$ for every $i = 1 \dots n$.

If no such permutation exists, print No.
If it exists, print Yes and on the next line output any permutation $p$ that satisfies the condition.

Constraints

• $1 \le t \le 10^4$
• $1 \le n \le 2 \times 10^5$
• The sum of $n$ over all test cases is at most $2 \times 10^5$