Problem Statement  
A sequence of numbers is called a zigzag 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 zigzag sequence. For example, 1,7,4,9,2,5 is a zigzag 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 zigzag 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 zigzag 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.  
Definition  
 
Constraints  
  sequence contains between 1 and 50 elements, inclusive.  
  Each element of sequence is between 1 and 1000, inclusive.  
Examples  
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