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.

import java.io.*;
import java.util.*;

public class CF_255_C_ALMOST_ARITHMETICAL_PROGRESSION {

	static TreeSet<Integer> [] map = new TreeSet [(int)1e6+1]; 
	
	public static void main(String[] args) throws Exception
	{
		Scanner sc = new Scanner();
		PrintWriter out = new PrintWriter(System.out);
		
		int n = sc.nextInt();
		
		int [] a = new int [n];
		
		for(int i = 0 ; i <= 1e6 ; i++)
			map[i] = new TreeSet<>();
		HashSet<Integer> set = new HashSet<>();
		
		for(int i = 0 ; i < n ;i++)
		{
			a[i] = sc.nextInt();
			map[a[i]].add(i);
			
			set.add(a[i]);
			
		}
		int [] diff = new int [set.size()];
		int index = 0 ;
		HashSet<Integer> set2 = new HashSet<>();
		
		for(int x : a) {
			if(set2.contains(x)) continue;
			diff[index++] = x ; 
			set2.add(x);
			
		}
		int ans = 1 ; 
		for(TreeSet<Integer>s : map)
			ans = Math.max(s.size(), ans);
		
		a = diff;
		n = a.length;
		
		for(int i = 0 ; i < n ; i++)
			for(int j = i + 1 ; j < n ; j++)
			{
				TreeSet<Integer> [] taken = new TreeSet[2];
				taken[0] = map[a[i]]; taken[1] = map[a[j]];
				
				int take = 0 , x = 0 ;
				Integer idx = -1 ;
				
				while(true)
				{
					idx = taken[x].higher(idx);
					
					if(idx == null) break; 
					
					take ++ ; 
					
					x ^= 1 ;
				}
				
				ans = Math.max(ans, take);
			}
		
		System.out.println(ans);
		
	}
	
	static class Scanner 
	{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st ; 
		
		String next() throws Exception
		{
			while(st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			
			return st.nextToken();
		}
		
		int nextInt () throws Exception
		{
			return Integer.parseInt(next());
		}
		
		long nextLong() throws Exception
		{
			return Long.parseLong(next());
		}
		
		boolean ready() throws Exception
		{
			return br.ready();
		}
	}

}
