The integer $n$, between 10000 and 99999, is represented as $abcde$ in decimal notation. The digits $a$, $b$, $c$, $d$, and $e$ are defined as follows:

- $a$ is the remainder when $n$ is divided by 2.
- $b$ is the remainder when $n$ is divided by 3.
- $c$ is the remainder when $n$ is divided by 4.
- $d$ is the remainder when $n$ is divided by 5.
- $e$ is the remainder when $n$ is divided by 6.

Find the value of $n$.

Let's think step by step and output the final answer within \boxed{}.
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