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.
#include <bits/stdc++.h>
using namespace std;
const long long MOD = 1000 * 1000 * 1000 + 7;
const long long INF = 2000ll * 1000 * 1000 * 1000 * 1000 * 1000;
const long long MAXN = 200000 + 4;
const long long MLOG = 22;
const long long NMAX = 350;
signed main() {
  ios_base ::sync_with_stdio(false);
  long long n;
  cin >> n;
  long long a[MAXN];
  map<long long, long long> mp;
  for (long long i = 0; i < n; i++) cin >> a[i];
  for (long long i = 0; i < n; i++) mp[a[i]]++;
  long long all = 1;
  map<pair<long long, long long>, bool> mm;
  for (long long i = 0; i < n; i++)
    for (long long j = 0; j < n; j++) {
      long long ans = 0;
      if (i == j) continue;
      long long x = a[i], xx = a[i];
      long long y = a[j], yy = a[j];
      if (mm[{x, y}]) continue;
      mm[{x, y}] = true;
      mp[x]--, ans++;
      mp[y]--, ans++;
      while (true) {
        swap(x, y);
        y += x;
        if (!mp[y]) break;
        mp[y]--, ans++;
      }
      all = max(all, ans);
      long long aannss = ans;
      aannss -= 2;
      mp[xx]++;
      mp[yy]++;
      while (aannss--) {
        swap(xx, yy);
        yy += xx;
        mp[yy]++;
      }
    }
  cout << max(all, mp[0]);
}
