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# 376. Wiggle Subsequence

## Description

A sequence of numbers is called a **wiggle 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 wiggle sequence.

For example, `[1,7,4,9,2,5]`

is a wiggle 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 wiggle sequences, the first because its first two differences are positive and the second because its last difference is zero.

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

**Example 1:**

Input:[1,7,4,9,2,5]Output:6Explanation:The entire sequence is a wiggle sequence.

**Example 2:**

Input:[1,17,5,10,13,15,10,5,16,8]Output:7Explanation:There are several subsequences that achieve this length. One is [1,17,10,13,10,16,8].

**Example 3:**

Input:[1,2,3,4,5,6,7,8,9]Output:2

**Follow up:**

Can you do it in O(*n*) time?