Score : $300$ points

Problem Statement

We have an empty box. Takahashi can cast the following two spells any number of times in any order.

• Spell $A$: puts one new ball into the box.
• Spell $B$: doubles the number of balls in the box.

Tell us a way to have exactly $N$ balls in the box with at most \mathbf{120} casts of spells. It can be proved that there always exists such a way under the Constraints given.

There is no way other than spells to alter the number of balls in the box.

Constraints

• $1 \leq N \leq 10^{18}$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

Output

Print a string $S$ consisting of A and B. The $i$-th character of $S$ should represent the spell for the $i$-th cast.

$S$ must have at most \mathbf{120} characters.

5

AABA

This changes the number of balls as follows: $0 \xrightarrow{A} 1\xrightarrow{A} 2 \xrightarrow{B}4\xrightarrow{A} 5$. There are also other acceptable outputs, such as AAAAA.

14

BBABBAAAB

This changes the number of balls as follows: $0 \xrightarrow{B} 0 \xrightarrow{B} 0 \xrightarrow{A}1 \xrightarrow{B} 2 \xrightarrow{B} 4 \xrightarrow{A}5 \xrightarrow{A}6 \xrightarrow{A} 7 \xrightarrow{B}14$. It is not required to minimize the length of $S$.