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;
int n, ans, cnt, maxn, minn;
int a[1010], dl[1010];
map<long long, int> Q;
int main() {
  scanf("%d", &n);
  maxn = -1000000000;
  minn = 1000000000;
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    if (!Q.count(a[i]))
      Q[a[i]] = 1;
    else
      Q[a[i]]++;
    maxn = max(a[i], maxn);
    minn = min(a[i], minn);
  }
  ans = 2;
  for (int i = 1; i <= n; i++)
    for (int j = 1; j <= n; j++)
      if (i != j) {
        Q[a[i]]--;
        Q[a[j]]--;
        cnt = 0;
        dl[++cnt] = a[i];
        dl[++cnt] = a[j];
        while (dl[cnt] + dl[cnt - 1] <= maxn && dl[cnt] + dl[cnt - 1] >= minn &&
               Q.count(dl[cnt] + dl[cnt - 1]) && Q[dl[cnt] + dl[cnt - 1]] > 0) {
          cnt++;
          dl[cnt] = dl[cnt - 1] + dl[cnt - 2];
          Q[dl[cnt - 1] + dl[cnt - 2]]--;
          if (!dl[cnt] && !dl[cnt - 1]) {
            ans = max(ans, cnt + Q[0]);
            break;
          }
        }
        ans = max(ans, cnt);
        while (cnt) Q[dl[cnt--]]++;
      }
  printf("%d\n", ans);
  return 0;
}
