Problem 21812 --Vawio Sequence

## 21812: Vawio Sequence

Time Limit: 1 Sec  Memory Limit: 65 MB
Submit: 17  Solved: 8
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## Description

Vawio Sequence is very funny，it is a sequence of integers. It has some interesting properties.
·   Vawio is of odd length i.e. L = 2*n + 1.
·  The first (n+1) integers of  Vawio sequence makes a strictly increasing sequence.
·  The last (n+1) integers of  Vawio sequence makes a strictly decreasing sequence.
·  No two adjacent integers are same in a  Vawio sequence.
For example 1, 2, 3, 4, 5, 4, 3, 2, 0 is an  Vawio sequence of length 9. But 1, 2, 3, 4, 5, 4, 3, 2, 2 is not a valid  Vawio sequence. In this problem, you will be given a sequence of integers. You have to find out the length of the longest  Vawio sequence which is a subsequence of the given sequence. Consider, the given sequence as :

1 2 3 2 1 2 3 4 3 2 1 5 4 1 2 3 2 2 1.

Here the longest Wavio sequence is : 1 2 3 4 5 4 3 2 1. So, the output will be 9.

## Input

The input file contains less than 75 test cases. The description of each test case is given below: Input is terminated by end of file.

Each set starts with a postive integer, N(1<=N<=10000). In next few lines there will be N integers

## Output

For each set of input print the length of longest Vawio sequence in a line.

## Sample Input

10
1 2 3 4 5 4 3 2 1 10
19
1 2 3 2 1 2 3 4 3 2 1 5 4 1 2 3 2 2 1
5
1 2 3 4 5


## Sample Output

9
9
1


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