P404239 - GYM101466 D Double it - SSOJ - 省实信息奥赛评测系统

Memory Limit：64 MB Time Limit：2 S

Judge Style：Text Compare Creator：

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D. Double ittime limit per test2 secondsmemory limit per test64 megabytesinputstandard inputoutputstandard output

Alex has two magic machines A and B. Machine A will give you 2x + 1 coins if you insert x coins in it, machine B will give you 2x + 2. Alex has no coins and wants to get exactly n coins in order to buy a new unicorn, but he can't figure out how to do it. Your task is to find a way to use the machines to get exactly n coins.

Input

The input consists of a single line containing n (1 ≤ n ≤ 10⁹).

Output

For each one output a string of A's and B's giving the order in which the machines are used.

ExamplesInput

Output

AAA

Input

Output

ABB

2017 ACM-ICPC, Universidad Nacional de Colombia Programming Contest

404239: GYM101466 D Double it

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