How many injective functions are there in $\mathbb{N}^\mathbb{N}$?

Question

I was wondering what's the cardinality of $\{f \in \mathbb{N}^\mathbb{N} \mid f \text{ is injective}\}$? I know it's uncountable, but what 'type' of uncountable? Is it the same cardinality of all surjective functions over $\mathbb{N}$? What about of all bijective functions over $\mathbb{N}$?

Thanks in advance!