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## Problem Description

Rar the cat has been observing mountains and has recorded the heights of a particular mountain range at every specific interval and recorded them into a list, forming a landscape. Now, he wants to process these data in order to make a better interpretation of the landscape. To do so, Rar the cat has decided to identify peaks. Rar the cat consider a place as a 1st-degree peak if the heights of the surroundings are strictly lower than itself. (Eg. 2 7 3, 7 will be the peak).

However this is not enough! A 1st-degree peak can be 'upgraded' to a 2nd-degree peak if the 2 adjacent 1st-degree peaks are lower than it. For example: If the heights recorded of the landscape are 2 5 3 7 4 1 6 2, then the 1st-degree peaks would be 5, 7 and 6. Since the 2 adjacent 1st-degree peaks of 7 is lower than itself, 7 is considered a 2nd-degree peak but 5 and 6 are still 1st-degree peaks.

Extending this rule, a *X*-degree peak can be 'upgraded' to a *X+1*-degree peak if the 2 adjacent *X*-degree peaks are lower than it.

Given the landscape, Rar the cat wants to know the degree of the highest degree peak.

## Input

A single integer, *N*. *N* denotes the number of positive integral heights that Rar the cat has recorded.

The following line consists of *N* integers, with each being in the range of 1 to 1000000000.

## Output

Output a single integer, the degree of the highest degree peak. If there are no 1st-degree peaks at all, then output 0 instead.

## Limits

Subtask 1 (35%): 0 < *N* ≤ 5000

Subtask 2 (65%): 0 < *N* ≤ 3000000

Subtask 3 (0%): As per sample testcases.

## Sample Testcase 1

Input:

8 2 5 3 7 4 1 6 2

Output:

2

## Sample Testcase 2

Input:

8 1 2 3 4 5 6 7 8

Output:

0

### Tags

### Subtasks and Limits

Subtask | Score | #TC | Time | Memory | Scoring |
---|---|---|---|---|---|

1 | 35 | 5 | 3s | 64MB | Minimum |

2 | 65 | 5 | 3s | 64MB | Minimum |

3 | 0 | 2 | 3s | 64MB | Minimum |

### Judge Compile Command

g++-8 ans.cpp -o peaks -Wall -Wshadow -static -O2 -lm -m64 -s -w -std=gnu++17 -fmax-errors=512