Find lim of the sequence

Find lim of the sequence

Let $(a_n)$ be a sequence where $a_1 \in \mathbb{R} $ and $a_{n+1}=\left |
a_n-2^{1-n} \right |,\forall n\in \mathbb{N}^*$ Find $\lim_{n \to +\infty
}{a_n}$