A sequence of integers whose values first increase and reach the peek, and then decrease is called bitonic. In this problem, we are looking at bitonic sequences of a given sequence.
Note: Increasing (and decreasing) doesn't include equal to. When it's increasing, the current number is definitely greater than the previous number.

Example:
The sequence 1 2 4 6 8 7 5 4 3 2 1 is bitonic, with number 8 being the peek. A sequence of this sequence is, say 1 6 5 1, but 8 2 6 is not a sequence.

Suppose that you are given an array of integers. You need to find the length of the longest bitonic sequence of the given sequence.

Question:
Write a program that gets as an input a positive number n and a sequence of n integers and computes the length of the longest bitonic sequence.

Input specification
You will be given an integer number (n) at the beginning where 1 ≤ n ≤ 50000. Then, in the following line, you will be given n integers which are between -10000 and 10000.

Output specification
Show just one integer: length of the longest bitonic sequence.

Explanation for Sample Input 2: The longest bitonic sequence is: 1 4 7 8 2 1 with the length 6.