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:
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 s_{1}, s_{2}, ..., s_{k} is a subsequence of sequence b_{1}, b_{2}, ..., b_{n}, if there is such increasing sequence of indexes i_{1}, i_{2}, ..., i_{k} (1 ≤ i_{1} < i_{2} < ... < 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 b_{1}, b_{2}, ..., b_{n} (1 ≤ b_{i} ≤ 10^{6}).