Problem3390--Almost Arithmetical Progression

3390: Almost Arithmetical Progression

Time Limit: 2 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
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Description

time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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·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,...,sk is a subsequence of sequence b1,b2,...,bn, if there is such increasing sequence of indexes i1,i2,...,ik (1≤i1<i2<... <ik≤n), that bij=sj. 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,...,bn (1≤bi≤106).

Output

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

Examples
Input
2
3 5
Output
2
Input
4
10 20 10 30
Output
3
Note

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

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

Source/Category

 
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