calculus - How to find this limit : $lim_{n to infty} frac{2-sqrt{2+sqrt{2 +sqrt{2+ cdots n text{ times}}}}}{4^{-n}}$

How to find this limit :

$$\lim_{n \to \infty} \frac{2-\sqrt{2+\sqrt{2 +\sqrt{2+ \cdots n \text{ times}}}}}{4^{-n}}$$

Please help not getting any idea how to solve this , will be of great help thanks.