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

public class Main{
		int n;
		int []a, next;
		int [][]mem;
		
		public void run(){
			Scanner in = new Scanner(System.in);
			n = in.nextInt();
			a = new int[n];
			for(int i=0;i<n;i++)
				a[i] = in.nextInt();
				
			next = new int[n];
			Arrays.fill(next, n);
			for(int i=0;i<n;i++)
				for(int j=i+1;j<n;j++)
					if (a[i] == a[j]){
						next[i] = j;
						break;
					}
			mem = new int[n][n];		
			for(int i=0;i<n;i++)
				Arrays.fill(mem[i], -1);
			
			int ans = 1;
			for(int i=n-1;i>=0;i--)
				for(int j=n-1;j>i;j--)
					ans = Math.max(ans, go(i,j));
					
			System.out.println(ans);
		}
		
		private int go(int i, int j){
			if (i > j)
				return go(j, i) + 1;
			if (j == n)
				return 1;
			if (mem[i][j] != -1)
				return mem[i][j];
			return mem[i][j] = go(next[i], j);
		}
	
		public static void main(String args[]){
			new Main().run();
		}
}
