A sequence of numbers is called a zig-zag sequence if the differences
between successive numbers strictly alternate between positive and
negative. The first difference (if one exists) may be either positive
or negative. A sequence with fewer than two elements is trivially a
zig-zag sequence.

For example, 1,7,4,9,2,5 is a zig-zag sequence because the differences
(6,-3,5,-7,3) are alternately positive and negative. In contrast,
1,4,7,2,5 and 1,7,4,5,5 are not zig-zag sequences, the first because
its first two differences are positive and the second because its last
difference is zero.

Given a sequence of integers, sequence, return the length of the
longest subsequence of sequence that is a zig-zag sequence. A
subsequence is obtained by deleting some number of elements (possibly
zero) from the original sequence, leaving the remaining elements in
their original order.

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