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; ai=ai-1+(-1)i+1 \cdot q (i \gt 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,...,sk is a subsequence of sequence b1,b2,...,bn, if there is such increasing sequence of indexes i1,i2,...,ik (1 \le i1 \lt i2 \lt ... \lt ik \le n), that bij=sj. In other words, sequence s can be obtained from b by crossing out some elements.

The first line contains integer n (1 \le n \le 4000). The next line contains n integers b1,b2,...,bn (1 \le bi \le 106).

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

In the first test the sequence actually is the suitable subsequence.

In the second test the following subsequence fits: 10,20,10.