LogiQuest

251. Longest Bitonic Subsequence

MediumDynamic Programming

A bitonic subsequence strictly increases then strictly decreases (either part may be empty). Print the length of the longest one.

Input format

Line 1: n Line 2: n integers

Output format

The length.

Example 1

Input

8
1 11 2 10 4 5 2 1

Output

6

Example 2

Input

6
12 11 40 5 3 1

Output

5

Constraints

1 ≤ n ≤ 2000

Read input from standard input and print the answer to standard output. Your code is judged against 4 test cases, most of them hidden.

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