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

public class D {
	FastScanner in;
	PrintWriter out;

	ArrayList<Integer> stack;
	HashMap<Integer, Integer> h;

	boolean contains(int x) {
		Integer res = h.get(x);
		return res != null && res != 0;
	}

	void restore() {
		for (int x : stack) {
			h.put(x, h.get(x) + 1);
		}
		stack.clear();
	}

	void remove(int x) {
		stack.add(x);
		h.put(x, h.get(x) - 1);
	}

	public void solve() throws IOException {
		int n = in.nextInt();
		h = new HashMap<>();
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			int x = a[i] = in.nextInt();
			if (!h.containsKey(x)) {
				h.put(x, 0);
			}
			h.put(x, h.get(x) + 1);
		}
		int ans = 2;
		boolean[] fzero = new boolean[n];
		for (int i = 0; i < n; i++) {
			if (a[i] == 0) {
				fzero[i] = true;
				break;
			}
		}
		HashSet<Long> was = new HashSet<>();
		long p = (long) (1e9 + 7);
		stack = new ArrayList<>();
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < n; j++) {
				if (i != j && !was.contains(a[i] * p + a[j])) {
					was.add(a[i] * p + a[j]);
					remove(a[i]);
					remove(a[j]);
					int cur = 2;
					int x = a[i], y = a[j];
					while (contains(y - x)) {
						int t = y - x;
						remove(t);
						y = x;
						x = t;
						cur++;
					}

					ans = Math.max(ans, cur);
					restore();
				}
			}
		}
		out.println(ans);
	}

	public void run() {
		try {
			in = new FastScanner();
			out = new PrintWriter(System.out);

			solve();

			out.close();
		} catch (IOException e) {
			e.printStackTrace();
		}
	}

	class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		FastScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}
	}

	public static void main(String[] arg) {
		new D().run();
	}
}