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.