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D - LR insertion

Score : $400$ points

Problem Statement

There is a sequence that contains one $0$, $A=(0)$.
Additionally, you are given a string of length $N$, $S=s_1s_2\ldots s_N$, consisting of L and R.

For each $i=1, 2, \ldots, N$ in this order, the following will be done.

• If $s_i$ is L, insert $i$ to the immediate left of $i-1$ in $A$.
• If $s_i$ is R, insert $i$ to the immediate right of $i-1$ in $A$.

Find the final contents of $A$.

Constraints

• $1\leq N \leq 5\times 10^5$
• $N$ is an integer.
• $|S| = N$
• $s_i$ is L or R.

Input

Input is given from Standard Input in the following format:

$N$

$S$

Output

Print the final contents of $A$, separated by spaces.

5
LRRLR

1 2 4 5 3 0

Initially, $A=(0)$.
$S_1$ is L, which makes it $A=(1,0)$.
$S_2$ is R, which makes it $A=(1,2,0)$.
$S_3$ is R, which makes it $A=(1,2,3,0)$.
$S_4$ is L, which makes it $A=(1,2,4,3,0)$.
$S_5$ is R, which makes it $A=(1,2,4,5,3,0)$.

7
LLLLLLL

7 6 5 4 3 2 1 0