If your answer is correct, that would be: 

115 quattuorvigintillion 792 trevigintillion 89 duovigintillion 237 unvigintillion 316 vigintillion 195 novemdecillion 423 octodecillion 570 septendecillion 985 sexdecillion 8 quindecillion 687 quattuordecillion 907 tredecillion 853 duodecillion 269 undecillion 984 decillion 665 nonillion 640 octillion 564 septillion 39 sextillion 457 quintillion 584 quadrillion 7 trillion 913 billion 129 million 639 thousand 936 

 Its a very big number 

 10^(256*log(2)/log(10)) ≈ 10^77 

 Because of reflections and a few invalid keys at the very top, it is only about half that.

So closer to 57896044618658097711785492504343953926634992332820282019728792003956564819968 

 I wondered if i'd get away with not mentioning that lol