4758 - [Usaco2017 Jan]Subsequence Reversal
Farmer John is arranging his NN cows in a line to take a photo (1≤N≤50). The height of the iith co w in sequence is a(i), and Farmer John thinks it would make for an aesthetically pleasing photo if t he cow lineup has a large increasing subsequence of cows by height.To recall, a subsequence is a sub set a(i1),a(i2),…,a(ik)) of elements from the cow sequence, found at some series of indices i1<i2< …<ik, We say the subsequence is increasing if a(i1)≤a(i2)≤…≤a(ik).FJ would like there to be a l ong increasing subsequence within his ordering of the cows. In order to ensure this, he allows himse lf initially to choose any subsequence and reverse its elements. For example, if we had the list 1 6 2 3 4 3 5 3 4 We can reverse the chosen elements 1 6 2 3 4 3 5 3 4 ^ ^ ^ ^ to get 1 4 2 3 4 3 3 5 6 ^ ^ ^ ^ Observe how the subsequence being reversed ends up using the same indices as it initially occupied, leaving the other elements unchanged.Please find the maximum possible length of an increasing subseq uence, given that you can choose to reverse an arbitrary subsequence once. 给定一个长度为N的序列，允许翻转一个子序列，求最长不下降子序列长度。n和数字都<=50
Input
The first line of input contains N. The remaining N lines contain a(1)…a(N), each an integer in the range 1…50.
Output
Output the number of elements that can possibly form a longest increasing subsequence after reversing the contents of at most one subsequence.
Examples
Input
9 1 2 3 9 5 6 8 7 4
Output
9