Longest Bitonic Subarray

A bitonic sequence is a sequence of numbers that first increase (non-decreasing) and then decreases (non-increasing). Given an array of integers, find the length of the longest subarray that is bitonic in nature.

Input

arr = [1, 2, 9, 5, 1, 2, 6, 7]

Output:

5

[5, 1, 2, 6, 7] is the longest bitonic subarray. Return its length, 5.

Input

arr = [3, 1, 2, 1, 4, 5]

Output:

3

[1, 2, 1] is the longest bitonic subarray. Note that the subarray [1, 4, 5] is also bitonic in nature and has the same length. It is non-decreasing through [1, 4, 5] and the non-increasing portion is [5].

Input

arr = [9, 7, 6, 2, 1]

Output:

5

The non-decreasing subarray is [9]. The non-increasing subarray is the entire array. The entire array has 5 elements.

Constraints

1 ≤ n ≤ 10^5  
1 ≤ arr[i] ≤ 10^9

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