Use two 2's, two 1's and two 8's to make the number 2018| Genius Will Get A Reward!

This is another number formation question. You must use each of 22, 11 and 88 exactly twice to make the number 20182018. The rules are

Allowed symbols: ++, −−, ××, ÷÷, ((, )), −−√, !!. Arbitrary functions (such as the logarithm) are not allowed.
The ordering of the numbers are not important.
It is OK to use numbers as superscript (exponent or the power for the radical symbol).
Concatenation is allowed although using (2+1)1(2+1)1 to construct 3131 is not allowed.
Ceiling or flooring is not allowed. 211÷2=105.5211÷2=105.5, not 105105 or 106106.
The use of decimal point or scientific notation is not allowed.

For example,
(2+8)×(2+1)!×1+8−−−−√=180