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;
long long int arr[10000];
map<long long int, long long int> mymap;
map<pair<long long int, long long int>, long long int> visited;
int main() {
  std::ios::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long int a, b, c, i, j, k, n, m;
  cin >> n;
  for (i = 0; i < n; i++) {
    cin >> arr[i];
    mymap[arr[i]] += 1;
  }
  long long int t1, t2, ans = 2, cnt = 0, tempt;
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      if (i == j) continue;
      t1 = arr[i];
      t2 = arr[j];
      if (visited[make_pair(t1, t2)] == 1) continue;
      visited[make_pair(t1, t2)] = 1;
      map<long long int, long long int> temp;
      temp[t1] += 1;
      temp[t2] += 1;
      cnt = 2;
      if (t1 == 0 && t2 == 0) {
        cnt = mymap[0];
        ans = max(ans, cnt);
        continue;
      }
      while (mymap[t1 + t2] - temp[t1 + t2] > 0) {
        temp[t1 + t2] += 1;
        tempt = t1 + t2;
        t1 = t2;
        t2 = tempt;
        cnt++;
      }
      ans = max(ans, cnt);
    }
  }
  cout << ans << endl;
  return 0;
}
