Fax and his squadrons attacking the base.

Fax McClad, Croneria's smartest bounty hunter, has found one of the Dankey Kang Gang's bases!

The Dankey Kang Gang base is made of a straight segment of ~N~ compartments numbered from ~1~ to ~N~ from left to right. The ~i^\text{th}~ compartment has a strength of ~s_i~. Let compartment ~-1~ and ~0~ be the space to the left of all other compartments.

Fax will attack the base using squadrons of Kyuwing bombers. Suppose Fax is over compartment ~i~. Then, Fax can issue the following commands:

• L - move to compartment ~i-1~. This command cannot be issued if Fax is over compartment ~-1~.
• A - if there is no squadron over compartment ~i+1~, order a new squadron to move to compartment ~i+1~. If there is already squadron over compartment ~i+1~, then that squadron retreats, which signals all other squadrons to the right (over compartments ~\ge i+2~) to drop their bombs on the compartments they are over and retreat.
• R - move to compartment ~i+1~. This command can only be issued if there is a squadron over compartment ~i+1~.

A compartment can only take ~s_i~ hits from bombs until it is destroyed.

Fax is initially to the left of all compartments (over compartment ~-1~).

What is the minimum number of commands that Fax must issue to destroy the base and what should they be?

Constraints

~1 \le N \le 2\,000~

~0 \le s_i \le 100~

At least one compartment will have ~s_i > 0~.

For ~20\%~ of the points, ~N \le 10~.

Input Specification

The first line of input will contain ~N~.

The next line will contain ~N~ integers. The ~i^\text{th}~ integer is ~s_i~.

Output Specification

On a single line, output a string consisting of L, A, and R, denoting the commands that he should issue, in order. You may output any answer of minimum length.

Sample Input

3
0 0 1

Sample Output

ARARARALA

Sample Explanation

The state when following the instructions will look like this:

--001   --001   --001   --001   --001   --001   --001   --001   --001   --000
         s       s       ss      ss      sss     sss     ssss    ssss    ss
^       ^        ^       ^        ^       ^        ^       ^      ^       ^

Note that compartment ~2~ was not hit by bombs.

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