Dont forget that you will need to go to Cairo twice, though.
Not necessarily... but one would need to end in the Middle East. From the OWE rules:
The continent of Europe-Middle East consists of 2 zones:
o Europe (including Algeria, Morocco, Russia west of the Urals and Tunisia)
o
Middle East (including Egypt, Libya and Sudan)
<snip>
(c)
Travel may originate at any point for which fares are published and must terminate at the same point, except that origin-destination surface segments are permitted as follows:
a. within the country of origin
b.
within the Middle East
c. between the United States and Canada
d. between HKG and China
e. between Malaysia and SIN
f. within Africa
g. between Maldives and Sri Lanka/India