P9015 [USACO23JAN] Moo Route S

Farmer Nhoj dropped Bessie in the middle of nowhere! At time $t=0$, Bessie is located at $x=0$ on an infinite number line. She frantically searches for an exit by moving left or right by $1$ unit each second. However, there actually is no exit and after $T$ seconds, Bessie is back at $x=0$, tired and resigned. Farmer Nhoj tries to track Bessie but only knows how many times Bessie crosses $x=0.5,1.5,2.5, \cdots ,(N−1).5$, given by an array $A_0,A_1, \cdots ,A_{N−1} (1 \le N \le 10^5, 1 \le A_i \le 10^6, \sum A_i \le 10^6)$. Bessie never reaches $x>N$ nor $x

The first line contains $N$. The second line contains $A_0,A_1,\cdots ,A_{N−1}$.

Output a string $S$ of length $T=\sum\limits_{i=0}^{N-1}A_i$ where $S_i$ is `L` or `R`, indicating the direction Bessie travels in during second $i$. If there are multiple routes minimizing the number of direction changes, output any.

### Explanation for Sample 1 There is only $1$ valid route, corresponding to the route $0 \rightarrow 1 \rightarrow 2 \rightarrow 1 \rightarrow 2 \rightarrow 1 \rightarrow 0$. Since this is the only possible route, it also has the minimum number of direction changes. ### Explanation for Sample 2 There are $3$ possible routes: RRLRRLRLLL RRRLRLLRLL RRRLLRRLLL The first two routes have $5$ direction changes, while the last one has only $3$. Thus the last route is the only correct output. ### Scoring - Inputs $3-5$: $N \le 2$ - Inputs $3-10$: $T=A_0+A_1+ \cdots +A_{N−1} \le 5000$ - Inputs $11-20$: No additional constraints.