Almost Arithmetical Progression - Problem

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_{i_j}=s_j. In other words, sequence s can be obtained from b by crossing out some elements.

Input

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

Output

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

Examples

Input

2
3 5

Output

Input

4
10 20 10 30

Output

Note

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

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

3619: Almost Arithmetical Progression

Description

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