Yash has recently learnt about the Fibonacci sequence and is very excited about it. He calls a sequence Fibonacci-ish if 

  1. the sequence consists of at least two elements 
  2. f0 and f1 are arbitrary 
  3. fn + 2 = fn + 1 + fn for all n ≥ 0. 



You are given some sequence of integers a1, a2, ..., an. Your task is rearrange elements of this sequence in such a way that its longest possible prefix is Fibonacci-ish sequence.

Input

The first line of the input contains a single integer n (2 ≤ n ≤ 1000) — the length of the sequence ai.

The second line contains n integers a1, a2, ..., an (|ai| ≤ 109).

Output

Print the length of the longest possible Fibonacci-ish prefix of the given sequence after rearrangement.

Examples

Input

3
1 2 -1


Output

3


Input

5
28 35 7 14 21


Output

4

Note

In the first sample, if we rearrange elements of the sequence as  - 1, 2, 1, the whole sequence ai would be Fibonacci-ish.

In the second sample, the optimal way to rearrange elements is <image>, <image>, <image>, <image>, 28.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.Scanner;
import java.util.Set;
import java.util.HashMap;
import java.util.ArrayList;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        public void solve(int testNumber, Scanner sc, PrintWriter out) {
            int n = sc.nextInt();
            int[] arr = new int[n];
            Map<Integer, Integer> counts = new HashMap<>();
            for (int i = 0; i < n; i++) {
                arr[i] = sc.nextInt();
                counts.put(arr[i], (counts.containsKey(arr[i]) ? counts.get(arr[i]) + 1 : 1));
            }

            Set<String> memo = new HashSet<>();
            int maxlen = 2;
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    if (i == j)
                        continue;

                    int a = arr[i];
                    int b = arr[j];
                    int need = a + b;

                    if (memo.contains(a + " " + b))
                        continue;
                    memo.add(a + " " + b);

                    List<Integer> seq = new ArrayList<>();
                    seq.add(a);
                    seq.add(b);
                    counts.put(a, counts.get(a) - 1);
                    counts.put(b, counts.get(b) - 1);
                    while (counts.containsKey(need) && counts.get(need) > 0) {
                        seq.add(need);
                        counts.put(need, counts.get(need) - 1);
                        a = b;
                        b = need;
                        need = a + b;
                    }

                    maxlen = Math.max(maxlen, seq.size());
                    for (int s : seq)
                        counts.put(s, counts.get(s) + 1);
                }
            }

            out.println(maxlen);
        }

    }
}
