Recycled Problem

The deadline for submitting problems for the finals of the 5th Cheonhajeil Coding Contest is one week away, but Jeonghwi has not even finished half of his problems. With the deadline closing in, he decides to recycle a problem from the preliminaries.

Specifically, he will combine the problems "Standing Tall on the High Namsan" and "Stand on the Foundation Stone" into a new problem.

A sequence $A_1, \cdots, A_N$ of length $N$ is a mountain if it increases up to some point and decreases after that point.

In other words, there is an index $i$ such that $A_{j-1} < A_j$ for every $j$ with $1 < j \le i$, and $A_{j-1} > A_j$ for every $j$ with $i < j \le N$.

Note that a sequence of length 1 is always a mountain.

Jeonghwi loves hiking, and he wants to find the length of the longest mountain among the contiguous subsequences of the sequence $A$.

A contiguous subsequence is a sequence $A_i, A_{i+1}, A_{i+2}, \cdots, A_j$ formed by choosing two indices $i, j$ with $1 \le i \le j \le N$.

Write a program that finds the length of the longest mountain so that Jeonghwi can hike as much as he wants.

The first line gives the length of the sequence, $N$.

The second line gives $N$ integers $A_1, A_2, \cdots, A_N$ separated by spaces.

Print the length of the longest mountain among the contiguous subsequences of the sequence $A$.

• $1 \leq N \leq 5\,000$
• $1 \leq A_i \leq 5\,000$

The contest was postponed by one month, and Jeonghwi was happy about it.