Arrow notation

Arrow Notation is a famous notation invented by Knuth in 1976 to represent large numbers.

Formula
$$a \uparrow b = a^b$$

$$a \uparrow\uparrow b = \underbrace{a \uparrow a \uparrow a \uparrow \ldots}_{b}$$

$$a \uparrow\uparrow\uparrow b = \underbrace{a \uparrow\uparrow a \uparrow\uparrow a \uparrow\uparrow \ldots}_{b}$$

$$a \uparrow\uparrow\uparrow\uparrow b = \underbrace{a \uparrow\uparrow\uparrow a \uparrow\uparrow\uparrow a \uparrow\uparrow\uparrow \ldots}_{b}$$

$$a \underbrace{\uparrow\uparrow\ldots\uparrow\uparrow}_c b = \underbrace{a \underbrace{\uparrow\uparrow\ldots\uparrow\uparrow}_{c - 1} a \underbrace{\uparrow\uparrow\ldots\uparrow\uparrow}_{c - 1} a \underbrace{\uparrow\uparrow\ldots\uparrow\uparrow}_{c - 1} \ldots}_{b}$$

Arrows are always calculated from right to left.

Examples

 * $$2 \uparrow 3 = 2^3 = 8$$
 * $$10 \uparrow 100 = 10^{100} =$$ googol
 * $$3 \uparrow\uparrow 4 = 3 \uparrow 3 \uparrow 3 \uparrow 3 = 3 \uparrow 3 \uparrow 27 = 3^{7625597484987}$$
 * $$2 \uparrow\uparrow\uparrow 2 = 2 \uparrow\uparrow 2 = 2 \uparrow 2 = 2^2 = 4$$
 * $$3 \uparrow\uparrow\uparrow 2 = 3 \uparrow\uparrow 3 = 3 \uparrow 3 \uparrow 3 = 3^{3^3} = 3^{27} = 7625597484987$$
 * $$2 \uparrow\uparrow\uparrow 3 = 2 \uparrow\uparrow 2 \uparrow\uparrow 2 = 2 \uparrow\uparrow 4 = 2 \uparrow 2 \uparrow 2 \uparrow 2 = 2 \uparrow 2 \uparrow 4 = 2 \uparrow 16 = 65536$$