Gena loves sequences of numbers. Recently, he has discovered a new type of sequences which he called an almost arithmetical progression. A sequence is an almost arithmetical progression, if its elements can be represented as:

• a₁=p, where p is some integer;
• a_i=a_i-1+(-1)ⁱ⁺¹·q (i>1), where q is some integer.

Right now Gena has a piece of paper with sequence b, consisting of n integers. Help Gena, find there the longest subsequence of integers that is an almost arithmetical progression.

Sequence s₁,s₂,...,s_k is a subsequence of sequence b₁,b₂,...,b_n, if there is such increasing sequence of indexes i₁,i₂,...,i_k (1≤i₁<i₂<... <i_k≤n), that b_ij=s_j. In other words, sequence s can be obtained from b by crossing out some elements.

The first line contains integer n (1≤n≤4000). The next line contains n integers b₁,b₂,...,b_n (1≤b_i≤10⁶).

Print a single integer − the length of the required longest subsequence.