Difference between revisions of "2028: Complex Numbers"
(Mentioned that addition is standard for vectors) |
X. K. C. D. (talk | contribs) |
||
Line 1: | Line 1: | ||
− | + | crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap 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Revision as of 01:31, 4 May 2022
crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap 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