Wavio Sequence

Wavio is a sequence of integers. It has some interesting properties.
  • Wavio is of odd length i.e. L = 2*n + 1.
  • The first (n+1) integers of Wavio sequence makes a strictly increasing sequence.
  • The last (n+1) integers of Wavio sequence makes a strictly decreasing sequence.
  • No two adjacent integers are same in a Wavio sequence.
    • For example 1, 2, 3, 4, 5, 4, 3, 2, 0 is an Wavio sequence of length 9. But 1, 2, 3, 4, 5, 4, 3, 2, 2 is not a valid wavio sequence. In this problem, you will be given a sequence of integers. You have to find out the length of the longest Wavio 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 wavio 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     		Output for Sample Input
    9
    9
    1