(a) How many of the 9000 four-digit integers 1000, 1001, 1002,..., 9998, 9999 have four distinct digits that are either increasing (as in 1347 and 6789) or decreasing (as in 6421 and 8653)?
(b) How many of the 9000 four-digit integers 1000, 1001, 1002...., 9998, 9999 have four digits that are either nondecreasing (as in 1347, 1226, and 7778) or nonincreasing (as in 6421, 6622, and 9888)?