Algorithm title: UVA 10534 Wavio Sequence (DP + LIS)

Wavio is a sequence of integers. It has some interesting properties.

· Wavio is of odd length i.e. L = 2*n + 1.

· The "n+1" integers of Wavio sequence makes a strictly increasing.

· The last (n+1) integers of Wavio sequence makes a strictly decreasing.

· No two adjacent integers are same in a wavio sequence.

For example 1, 2, 3, 4, 5, 4, 3, 2, 0 are an wavio sequence of length 9. But 1, 2, 3, 4, 5, 4, 3, 2, 2 are not a valid Wavio sequence. In this problem, you'll be given a sequence of integers. You are have to find the length of the longest Wavio sequence which is a subsequence of the given. Consider, the given sequence as:

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

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

Input

The input file contains less than test cases. The description of each test case is given Below:input was terminated by end of.

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

Output

For each set of input print the length of longest wavio sequence in a line.
Sample input Output for sample input

Problemsetter:md. Kamruzzaman, member of the Elite problemsetters ' Panel