D - Gathering Children

Score : $400$ points

Problem Statement

Given is a string $S$ consisting of L and R.

Let $N$ be the length of $S$. There are $N$ squares arranged from left to right, and the $i$-th character of $S$ from the left is written on the $i$-th square from the left.

The character written on the leftmost square is always R, and the character written on the rightmost square is always L.

Initially, one child is standing on each square.

Each child will perform the move below $10^{100}$ times:

• Move one square in the direction specified by the character written in the square on which the child is standing. L denotes left, and R denotes right.

Find the number of children standing on each square after the children performed the moves.

Constraints

• $S$ is a string of length between $2$ and $10^5$ (inclusive).
• Each character of $S$ is L or R.
• The first and last characters of $S$ are R and L, respectively.

Input

Input is given from Standard Input in the following format:

$S$

Output

Print the number of children standing on each square after the children performed the moves, in order from left to right.

RRLRL

0 1 2 1 1

• After each child performed one move, the number of children standing on each square is $0, 2, 1, 1, 1$ from left to right.
• After each child performed two moves, the number of children standing on each square is $0, 1, 2, 1, 1$ from left to right.
• After each child performed $10^{100}$ moves, the number of children standing on each square is $0, 1, 2, 1, 1$ from left to right.

RRLLLLRLRRLL

0 3 3 0 0 0 1 1 0 2 2 0

RRRLLRLLRRRLLLLL

0 0 3 2 0 2 1 0 0 0 4 4 0 0 0 0