# Problem E

Wizard Dance

Author: unknown, no known restrictions

In the USA, a type of dance called *square dance* is
very popular. Four dancing pairs stand as to form a square. A
*caller* then gives a series of moves that the dancers
should perform, moving around on the floor.

American wizards, however, find square dancing a bit
simplistic. Instead, they have come up with a kind of dance
called *circle dancing*. In the dance, $N$ wizards stand in a circle numbered
$1$ through $N$ clockwise. A caller then gives a
series of moves that the dancers should perform, moving around
on the floor. Each such move has the following form. Every
wizard is given a number $p_
i$. They then all teleport simultaneously $p_ i$ positions clockwise or
counterclockwise in the ring. For example, given the number 1
they should move to one of the two places immediately adjacent
to their current position.

After a move is performed, no two wizards may occupy the same position. This means a certain amount of coordination is required when teleporting. Can you tell the wizards how they should teleport in order to not collide with each other?

## Input

The first line of input contains a single integer $N$ ($1 \le N \le 300\, 000$), the number of wizards. The next line contains the $N$ integers $p_1, p_2, \dots , p_ N$ ($0 \le p_ i < N$). The wizards are numbered $1, 2, \dots , N$ clockwise in the circle.

## Output

Output a string with $N$ characters. The $i$’th character should be `L` if the $i$’th wizard should teleport
clockwise, and `R` if he should
teleport counterclockwise. If there are multiple valid
solutions, output the *lexicographically smallest one*.
If there is no valid solution, output `no
dance`.

Sample Input 1 | Sample Output 1 |
---|---|

3 1 1 1 |
LLL |

Sample Input 2 | Sample Output 2 |
---|---|

5 1 2 2 1 2 |
LLRLR |

Sample Input 3 | Sample Output 3 |
---|---|

4 1 2 1 2 |
no dance |