Is this number, N, greater than Graham’s Number?

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So, using Knuth’s up-arrow notation,
if 3 ↑ 3 = 3^3 and 3 ↑ ↑ 3 = 3 ↑ (3 ↑ 3) = 3 ↑ 27 = 3^27

Then consider number N defined by Knuth's up-arrow notation:
$$N = googolplex\uparrow^{googolplex} googolplex$$

Is the number $N$ greater than Graham’s Number or is it even possible to determine this?