So far I have revived $89$ out of the first $120$ numbers, with $78$ being in the first $100$.
I will keep editing. Please note that I have not used spoilers since this is too laggy - sorry for the inconvenience. Here is the partial answer:
$\left\lfloor\sqrt{\sqrt{2.6854}}\right\rfloor=1$
$\left\lceil \sqrt{2.6854} \right\rceil=2$
$\left\lceil 2.6854 \right\rceil = 3$
$\left\lceil\sqrt{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor}\right\rceil= 4$
$\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor= 5$
$\left(\left\lceil 2.6854 \right\rceil\right)! = 6$
$\left\lceil\sqrt{\left \lceil \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rceil}\right\rceil= 7$
$\left \lfloor \sqrt[2^2]{\left\{\left\lceil\sqrt{\left \lceil \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rceil}\right\rceil\right\}!} \right \rfloor= 8$
$\left \lceil \sqrt[2^2]{\left\{\left\lceil\sqrt{\left \lceil \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rceil}\right\rceil\right\}!} \right \rceil= 9$
$\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor= 10$
$\left\lceil\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rceil= 11$
$\left \lfloor\sqrt[2^5]{\left\{\left \lfloor \sqrt[2^3]{\left\{\left \lceil \sqrt[2^2]{\left\{\left \lfloor \sqrt[2^2]{\left\{\left\lceil\sqrt{\left \lceil \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rceil}\right\rceil\right\}!} \right \rfloor\right\}!} \right \rceil\right\}!} \right \rfloor\right\}!}\right\rfloor= 12$
$\left \lfloor\sqrt[2^7]{\left\{\left\lfloor\sqrt[2^3]{\left\{\left \lceil\sqrt[2^4]{\left\{\left \lfloor \sqrt[2^7]{\left\{\left \lfloor\sqrt[2^4]{\left\{\left\lfloor\sqrt[2^4]{\left\{\left\{\left\lceil\sqrt{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor}\right\rceil\right\}!\right\}!} \right\rfloor\right\}!} \right \rfloor\right\}!} \right \rfloor\right\}!} \right\rceil\right\}!}\right\rfloor\right\}!} \right\rfloor= 13$
$\left \lfloor \sqrt[2^2]{\left\{\left \lfloor \sqrt[2^2]{\left\{\left\lceil\sqrt{\left \lceil \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rceil}\right\rceil\right\}!} \right \rfloor\right\}!} \right \rfloor= 14$
$\left \lceil \sqrt[2^2]{\left\{\left \lfloor \sqrt[2^2]{\left\{\left\lceil\sqrt{\left \lceil \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rceil}\right\rceil\right\}!} \right \rfloor\right\}!} \right \rceil= 15$
$\left \lceil\sqrt[2^6]{\left\{\left \lceil\sqrt[2^4]{\left\{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil\right\}!}\right \rceil\right\} !} \right \rceil= 16$
$\left \lfloor\sqrt[2^4]{\left\{\left \lfloor \sqrt[2^7]{\left\{\left \lfloor\sqrt[2^4]{\left\{\left\lfloor\sqrt[2^4]{\left\{\left\{\left\lceil\sqrt{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor}\right\rceil\right\}!\right\}!} \right\rfloor\right\}!} \right \rfloor\right\}!} \right \rfloor\right\}!} \right\rfloor= 17$
$\left \lceil\sqrt[2^4]{\left\{\left \lfloor \sqrt[2^7]{\left\{\left \lfloor\sqrt[2^4]{\left\{\left\lfloor\sqrt[2^4]{\left\{\left\{\left\lceil\sqrt{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor}\right\rceil\right\}!\right\}!} \right\rfloor\right\}!} \right \rfloor\right\}!} \right \rfloor\right\}!} \right\rceil= 18$
$\left\lceil\sqrt[2^7]{\left\{\left \lfloor\sqrt[2^{13}]{\left\{\left\{\left\lceil\sqrt{\left \lceil \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rceil}\right\rceil\right\}!\right\}!}\right \rfloor\right\}!}\right\rceil= 19$
$\left \lfloor\sqrt[2^4]{\left\{\left \lceil \sqrt[2^7]{\left\{\left \lfloor\sqrt[2^4]{\left\{\left\lfloor\sqrt[2^4]{\left\{\left\{\left\lceil\sqrt{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor}\right\rceil\right\}!\right\}!} \right\rfloor\right\}!} \right \rfloor\right\}!} \right \rceil\right\}!} \right\rfloor= 20$
$\left \lfloor \sqrt[2^7]{\left\{\left \lfloor\sqrt[2^4]{\left\{\left\lfloor\sqrt[2^4]{\left\{\left\{\left\lceil\sqrt{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor}\right\rceil\right\}!\right\}!} \right\rfloor\right\}!} \right \rfloor\right\}!} \right \rfloor= 21$
$\left \lceil \sqrt[2^7]{\left\{\left \lfloor\sqrt[2^4]{\left\{\left\lfloor\sqrt[2^4]{\left\{\left\{\left\lceil\sqrt{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor}\right\rceil\right\}!\right\}!} \right\rfloor\right\}!} \right \rfloor\right\}!} \right \rceil= 22$
$\left \lfloor\sqrt[2^3]{\left\{\left \lfloor \sqrt[2^2]{\left\{\left \lfloor \sqrt[2^2]{\left\{\left\lceil\sqrt{\left \lceil \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rceil}\right\rceil\right\}!} \right \rfloor\right\}!} \right \rfloor\right\}!} \right\rfloor=23$
$\left\{\left\lceil\sqrt{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor}\right\rceil\right\}!= 24$
$\left \lceil\sqrt[2^2]{\left\{\left \lceil \sqrt[2^2]{\left\{\left\lceil\sqrt{\left \lceil \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rceil}\right\rceil\right\}!} \right \rceil\right\}!} \right\rceil= 25$
$\left\lfloor \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rfloor= 26$
$\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil= 27$
$\left\lfloor \sqrt[2^6]{\left\{\left \lceil\sqrt[2^3]{\left\{\left \lfloor\sqrt[2^4]{\left\{\left \lfloor \sqrt[2^7]{\left\{\left \lfloor\sqrt[2^4]{\left\{\left\lfloor\sqrt[2^4]{\left\{\left\{\left\lceil\sqrt{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor}\right\rceil\right\}!\right\}!} \right\rfloor\right\}!} \right \rfloor\right\}!} \right \rfloor\right\}!} \right\rfloor\right\}!} \right\rceil\right\}!}\right\rfloor= 28$
$\left\lceil \sqrt[2^6]{\left\{\left \lceil\sqrt[2^3]{\left\{\left \lfloor\sqrt[2^4]{\left\{\left \lfloor \sqrt[2^7]{\left\{\left \lfloor\sqrt[2^4]{\left\{\left\lfloor\sqrt[2^4]{\left\{\left\{\left\lceil\sqrt{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor}\right\rceil\right\}!\right\}!} \right\rfloor\right\}!} \right \rfloor\right\}!} \right \rfloor\right\}!} \right\rfloor\right\}!} \right\rceil\right\}!}\right\rceil= 29$
$\left\lfloor\sqrt[2^4]{\left\{\left\{\left\lceil\sqrt{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor}\right\rceil\right\}!\right\}!} \right\rfloor= 30$
$\left\lceil\sqrt[2^4]{\left\{\left\{\left\lceil\sqrt{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor}\right\rceil\right\}!\right\}!} \right\rceil= 31$
$\left \lfloor \sqrt[2^3]{\left\{\left \lceil \sqrt[2^2]{\left\{\left \lfloor \sqrt[2^2]{\left\{\left\lceil\sqrt{\left \lceil \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rceil}\right\rceil\right\}!} \right \rfloor\right\}!} \right \rceil\right\}!} \right \rfloor= 32$
$\left \lceil \sqrt[2^3]{\left\{\left \lceil \sqrt[2^2]{\left\{\left \lfloor \sqrt[2^2]{\left\{\left\lceil\sqrt{\left \lceil \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rceil}\right\rceil\right\}!} \right \rfloor\right\}!} \right \rceil\right\}!} \right \rceil= 33$
$\left \lceil\sqrt[2^7]{\left\{\left \lceil\sqrt[2^5]{\left \{ \left \lceil\sqrt[2^5]{\left \{\left \lceil \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rceil \right\} !} \right\rceil \right \}!} \right \rceil\right\}!}\right \rceil= 34$
$\left \lfloor \sqrt[2^7]{\left\{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!\right\}!} \right\rfloor= 35$
$\left \lfloor \sqrt[2^6]{\left\{\left \lfloor\sqrt{\left\{\left\lceil\sqrt{\left \lceil \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rceil}\right\rceil\right\}!} \right\rfloor\right\}!}\right\rfloor= 36$
$\left \lfloor \sqrt[2^4]{\left \{\left \lceil\sqrt[2^2]{\left\{\left \lceil \sqrt[2^2]{\left\{\left\lceil\sqrt{\left \lceil \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rceil}\right\rceil\right\}!} \right \rceil\right\}!} \right\rceil \right \}!} \right \rfloor= 37$
$\left \lceil \sqrt[2^4]{\left \{\left \lceil\sqrt[2^2]{\left\{\left \lceil \sqrt[2^2]{\left\{\left\lceil\sqrt{\left \lceil \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rceil}\right\rceil\right\}!} \right \rceil\right\}!} \right\rceil \right \}!} \right \rceil= 38$
$\left \lfloor \sqrt[2^6]{\left \{ \left \lceil\sqrt{\left\{\left\lceil\sqrt{\left \lceil \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rceil}\right\rceil\right\}!} \right\rceil\right \}!} \right \rfloor= 39$
$\left \lceil \sqrt[2^6]{\left \{ \left \lceil\sqrt{\left\{\left\lceil\sqrt{\left \lceil \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rceil}\right\rceil\right\}!} \right\rceil\right \}!} \right \rceil= 40$
$\left \lfloor \sqrt[2^6]{\left \{\left\lceil\sqrt[2^5]{\left\{\left\lceil\sqrt[2^4]{\left\{\left\lfloor \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rfloor\right\}!}\right\rceil\right\}!}\right\rceil \right\}!} \right \rfloor= 41$
$\left \lceil \sqrt[2^6]{\left \{\left\lceil\sqrt[2^5]{\left\{\left\lceil\sqrt[2^4]{\left\{\left\lfloor \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rfloor\right\}!}\right\rceil\right\}!}\right\rceil \right\}!} \right \rceil= 42$
$\left \lfloor \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rfloor= 43$
$\left \lceil \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rceil= 44$
$\left \lceil \sqrt[2^5]{\left\{ \left \lfloor \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rfloor\right\}!} \right \rceil= 45$
$\left\lfloor\sqrt[2^4]{\left\{\left\lfloor \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rfloor\right\}!}\right\rfloor= 46$
$\left\lceil\sqrt[2^4]{\left\{\left\lfloor \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rfloor\right\}!}\right\rceil= 47$
$\small \left\lfloor\sqrt[2^{35}]{\left\{\left\{\left \lfloor\sqrt[2^7]{\left\{\left\lfloor\sqrt[2^3]{\left\{\left \lceil\sqrt[2^4]{\left\{\left \lfloor \sqrt[2^7]{\left\{\left \lfloor\sqrt[2^4]{\left\{\left\lfloor\sqrt[2^4]{\left\{\left\{\left\lceil\sqrt{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor}\right\rceil\right\}!\right\}!} \right\rfloor\right\}!} \right \rfloor\right\}!} \right \rfloor\right\}!} \right\rceil\right\}!}\right\rfloor\right\}!} \right\rfloor\right\}!\right\}!} \right\rfloor= 49$
$\left \lfloor\sqrt[2^5]{\left \{\left \lceil \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rceil \right\} !} \right\rfloor= 50$
$\left \lceil\sqrt[2^5]{\left \{\left \lceil \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rceil \right\} !} \right\rceil= 51$
$\left\lfloor\sqrt[2^{43}]{\left\{\left\{\left \lceil \sqrt[2^2]{\left\{\left \lfloor \sqrt[2^2]{\left\{\left\lceil\sqrt{\left \lceil \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rceil}\right\rceil\right\}!} \right \rfloor\right\}!} \right \rceil\right\}!\right\}!}\right\rfloor= 54$
$\left\lceil\sqrt[2^{43}]{\left\{\left\{\left \lceil \sqrt[2^2]{\left\{\left \lfloor \sqrt[2^2]{\left\{\left\lceil\sqrt{\left \lceil \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rceil}\right\rceil\right\}!} \right \rfloor\right\}!} \right \rceil\right\}!\right\}!}\right\rceil= 55$
$\left \lfloor\sqrt[2^4]{\left\{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil\right\}!}\right \rfloor= 56$
$\left \lceil\sqrt[2^4]{\left\{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil\right\}!}\right \rceil= 57$
$\left\lfloor\sqrt[2^{11}]{\left\{\left\lfloor\sqrt[2^5]{\left\{\left \lfloor\sqrt{\left\{\left\lceil\sqrt{\left \lceil \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rceil}\right\rceil\right\}!} \right\rfloor\right\}!}\right\rfloor\right\}!} \right\rfloor= 58$
$\left \lfloor\sqrt[2^{20}]{\left\{\left\{\left \lceil \sqrt[2^2]{\left\{\left\lceil\sqrt{\left \lceil \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rceil}\right\rceil\right\}!} \right \rceil\right\}!\right\}!} \right \rfloor= 59$
$\left \lceil\sqrt[2^{20}]{\left\{\left\{\left \lceil \sqrt[2^2]{\left\{\left\lceil\sqrt{\left \lceil \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rceil}\right\rceil\right\}!} \right \rceil\right\}!\right\}!} \right \rceil= 60$
$\left\lceil \sqrt[2^6]{\left\{\left\lceil\sqrt[2^6]{\left\{\left\lceil\sqrt[2^8]{\left\{\left\lceil\sqrt[2^5]{\left\{\left \lceil\sqrt[2^4]{\left\{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil\right\}!}\right \rceil\right\}!}\right\rceil\right\}!}\right\rceil\right\}!}\right\rceil\right\}!}\right\rceil= 62$
$\left \lfloor\sqrt[2^5]{\left\{\left\lfloor\sqrt[2^4]{\left\{\left\lfloor \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rfloor\right\}!}\right\rfloor\right\}!} \right \rfloor= 63$
$\left \lceil\sqrt[2^5]{\left\{\left\lfloor\sqrt[2^4]{\left\{\left\lfloor \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rfloor\right\}!}\right\rfloor\right\}!} \right \rceil= 64$
$\left \lfloor\sqrt[2^3]{\left\{\left \lfloor\sqrt[2^4]{\left\{\left \lfloor \sqrt[2^7]{\left\{\left \lfloor\sqrt[2^4]{\left\{\left\lfloor\sqrt[2^4]{\left\{\left\{\left\lceil\sqrt{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor}\right\rceil\right\}!\right\}!} \right\rfloor\right\}!} \right \rfloor\right\}!} \right \rfloor\right\}!} \right\rfloor\right\}!} \right\rfloor= 65$
$\left \lceil\sqrt[2^3]{\left\{\left \lfloor\sqrt[2^4]{\left\{\left \lfloor \sqrt[2^7]{\left\{\left \lfloor\sqrt[2^4]{\left\{\left\lfloor\sqrt[2^4]{\left\{\left\{\left\lceil\sqrt{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor}\right\rceil\right\}!\right\}!} \right\rfloor\right\}!} \right \rfloor\right\}!} \right \rfloor\right\}!} \right\rfloor\right\}!} \right\rceil= 66$
$\left \lfloor\sqrt[2^6]{\left\{\left \lfloor\sqrt[2^2]{\left\{\left\lceil\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rceil\right\}!} \right \rfloor\right\}!} \right \rfloor= 67$
$\left \lceil\sqrt[2^6]{\left\{\left \lfloor\sqrt[2^2]{\left\{\left\lceil\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rceil\right\}!} \right \rfloor\right\}!} \right \rceil= 68$
$\left\lfloor \sqrt[2^4]{\left\{\left\lfloor \sqrt[2^6]{\left\{\left \lceil\sqrt[2^3]{\left\{\left \lfloor\sqrt[2^4]{\left\{\left \lfloor \sqrt[2^7]{\left\{\left \lfloor\sqrt[2^4]{\left\{\left\lfloor\sqrt[2^4]{\left\{\left\{\left\lceil\sqrt{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor}\right\rceil\right\}!\right\}!} \right\rfloor\right\}!} \right \rfloor\right\}!} \right \rfloor\right\}!} \right\rfloor\right\}!} \right\rceil\right\}!}\right\rfloor\right\}!} \right\rfloor= 69$
$\left \lfloor\sqrt{\left\{\left\lceil\sqrt{\left \lceil \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rceil}\right\rceil\right\}!} \right\rfloor= 70$
$\left \lceil\sqrt{\left\{\left\lceil\sqrt{\left \lceil \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rceil}\right\rceil\right\}!} \right\rceil= 71$
$\left\lceil\sqrt[2^5]{\left\{\left\lceil\sqrt[2^4]{\left\{\left\lfloor \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rfloor\right\}!}\right\rceil\right\}!}\right\rceil= 72$
$\left\lceil\sqrt[2^6]{\left\{\left\lceil\sqrt[2^8]{\left\{\left\lceil\sqrt[2^5]{\left\{\left \lceil\sqrt[2^4]{\left\{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil\right\}!}\right \rceil\right\}!}\right\rceil\right\}!}\right\rceil\right\}!}\right\rceil= 78$
$\left \lfloor\sqrt[2^2]{\left\{\left\lceil\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rceil\right\}!} \right \rfloor= 79$
$\left \lceil\sqrt[2^2]{\left\{\left\lceil\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rceil\right\}!} \right \rceil= 80$
$\left\lceil\sqrt[2^8]{\left\{\left\lceil\sqrt[2^5]{\left\{\left \lceil\sqrt[2^4]{\left\{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil\right\}!}\right \rceil\right\}!}\right\rceil\right\}!}\right\rceil= 81$
$\left\lfloor\sqrt[2^{47}]{\left\{\left\{\left \lceil\sqrt[2^6]{\left\{\left \lceil\sqrt[2^4]{\left\{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil\right\}!}\right \rceil\right\} !} \right \rceil\right\}!\right\}!}\right\rfloor= 82$
$\left\lceil\sqrt[2^{47}]{\left\{\left\{\left \lceil\sqrt[2^6]{\left\{\left \lceil\sqrt[2^4]{\left\{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil\right\}!}\right \rceil\right\} !} \right \rceil\right\}!\right\}!}\right\rceil= 83$
$\left\lfloor\sqrt[2^4]{\left\{\left\lceil \sqrt[2^6]{\left\{\left \lceil\sqrt[2^3]{\left\{\left \lfloor\sqrt[2^4]{\left\{\left \lfloor \sqrt[2^7]{\left\{\left \lfloor\sqrt[2^4]{\left\{\left\lfloor\sqrt[2^4]{\left\{\left\{\left\lceil\sqrt{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor}\right\rceil\right\}!\right\}!} \right\rfloor\right\}!} \right \rfloor\right\}!} \right \rfloor\right\}!} \right\rfloor\right\}!} \right\rceil\right\}!}\right\rceil\right\}!}\right\rfloor= 85$
$\left\lceil\sqrt[2^4]{\left\{\left\lceil \sqrt[2^6]{\left\{\left \lceil\sqrt[2^3]{\left\{\left \lfloor\sqrt[2^4]{\left\{\left \lfloor \sqrt[2^7]{\left\{\left \lfloor\sqrt[2^4]{\left\{\left\lfloor\sqrt[2^4]{\left\{\left\{\left\lceil\sqrt{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor}\right\rceil\right\}!\right\}!} \right\rfloor\right\}!} \right \rfloor\right\}!} \right \rfloor\right\}!} \right\rfloor\right\}!} \right\rceil\right\}!}\right\rceil\right\}!}\right\rceil= 86$
$\left\lfloor\sqrt[2^3]{\left\{\left \lceil\sqrt[2^4]{\left\{\left \lfloor \sqrt[2^7]{\left\{\left \lfloor\sqrt[2^4]{\left\{\left\lfloor\sqrt[2^4]{\left\{\left\{\left\lceil\sqrt{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor}\right\rceil\right\}!\right\}!} \right\rfloor\right\}!} \right \rfloor\right\}!} \right \rfloor\right\}!} \right\rceil\right\}!}\right\rfloor= 94$
$\left\lceil\sqrt[2^3]{\left\{\left \lceil\sqrt[2^4]{\left\{\left \lfloor \sqrt[2^7]{\left\{\left \lfloor\sqrt[2^4]{\left\{\left\lfloor\sqrt[2^4]{\left\{\left\{\left\lceil\sqrt{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor}\right\rceil\right\}!\right\}!} \right\rfloor\right\}!} \right \rfloor\right\}!} \right \rfloor\right\}!} \right\rceil\right\}!}\right\rceil= 95$
$\small \left \lfloor \sqrt[2^6]{\left\{\left\lfloor\sqrt[2^4]{\left\{\left\lceil \sqrt[2^6]{\left\{\left \lceil\sqrt[2^3]{\left\{\left \lfloor\sqrt[2^4]{\left\{\left \lfloor \sqrt[2^7]{\left\{\left \lfloor\sqrt[2^4]{\left\{\left\lfloor\sqrt[2^4]{\left\{\left\{\left\lceil\sqrt{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor}\right\rceil\right\}!\right\}!} \right\rfloor\right\}!} \right \rfloor\right\}!} \right \rfloor\right\}!} \right\rfloor\right\}!} \right\rceil\right\}!}\right\rceil\right\}!}\right\rfloor\right\}!} \right\rfloor= 101$
$\left \lfloor\sqrt[2^{13}]{\left\{\left\{\left\lceil\sqrt{\left \lceil \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rceil}\right\rceil\right\}!\right\}!}\right \rfloor= 102$
$\left \lceil\sqrt[2^{13}]{\left\{\left\{\left\lceil\sqrt{\left \lceil \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rceil}\right\rceil\right\}!\right\}!}\right \rceil= 103$
$\left\lceil\sqrt[2^5]{\left\{\left \lfloor\sqrt[2^5]{\left \{\left \lceil \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rceil \right\} !} \right\rfloor\right\}!}\right\rceil= 104$
$\left \lfloor\sqrt[2^4]{\left\{\left\lfloor\sqrt[2^4]{\left\{\left\{\left\lceil\sqrt{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor}\right\rceil\right\}!\right\}!} \right\rfloor\right\}!} \right \rfloor= 106$
$\left \lceil\sqrt[2^4]{\left\{\left\lfloor\sqrt[2^4]{\left\{\left\{\left\lceil\sqrt{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor}\right\rceil\right\}!\right\}!} \right\rfloor\right\}!} \right \rceil= 107$
$\small\left\lfloor\sqrt[2^6]{\left\{\left\lceil\sqrt[2^4]{\left\{\left\lceil \sqrt[2^6]{\left\{\left \lceil\sqrt[2^3]{\left\{\left \lfloor\sqrt[2^4]{\left\{\left \lfloor \sqrt[2^7]{\left\{\left \lfloor\sqrt[2^4]{\left\{\left\lfloor\sqrt[2^4]{\left\{\left\{\left\lceil\sqrt{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor}\right\rceil\right\}!\right\}!} \right\rfloor\right\}!} \right \rfloor\right\}!} \right \rfloor\right\}!} \right\rfloor\right\}!} \right\rceil\right\}!}\right\rceil\right\}!}\right\rceil\right\}!}\right\rfloor= 108$
$\small\left\lceil\sqrt[2^6]{\left\{\left\lceil\sqrt[2^4]{\left\{\left\lceil \sqrt[2^6]{\left\{\left \lceil\sqrt[2^3]{\left\{\left \lfloor\sqrt[2^4]{\left\{\left \lfloor \sqrt[2^7]{\left\{\left \lfloor\sqrt[2^4]{\left\{\left\lfloor\sqrt[2^4]{\left\{\left\{\left\lceil\sqrt{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor}\right\rceil\right\}!\right\}!} \right\rfloor\right\}!} \right \rfloor\right\}!} \right \rfloor\right\}!} \right\rfloor\right\}!} \right\rceil\right\}!}\right\rceil\right\}!}\right\rceil\right\}!}\right\rceil= 109$
$\left \lfloor\sqrt[2^5]{\left \{ \left \lceil\sqrt[2^5]{\left \{\left \lceil \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rceil \right\} !} \right\rceil \right \}!} \right \rfloor= 117$
$\left \lceil\sqrt[2^5]{\left \{ \left \lceil\sqrt[2^5]{\left \{\left \lceil \sqrt[2^2]{\left\{\left\lfloor\sqrt{\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!}\right\rfloor\right\}!} \right \rceil \right\} !} \right\rceil \right \}!} \right \rceil= 118$
$\left[\left\lfloor\sqrt{\left\lceil \sqrt{(\left(\left\lceil 2.6854 \right\rceil\right)!)!} \right\rceil}\right\rfloor\right]!=120$