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 int MAXN = 1e5 + 5;
int n;
int a[1005];
map<int, int> mp;
map<pair<int, int>, int> used;
inline int read() {
  int x = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = (x << 1) + (x << 3) + (ch ^ 48);
    ch = getchar();
  }
  return x * f;
}
int check(int na, int nb) {
  int fd = na + nb;
  if (mp[fd] == 0) return 0;
  mp[fd]--;
  int sum = check(nb, fd);
  mp[fd]++;
  return 1 + sum;
}
int main(int argc, char* argv[]) {
  n = read();
  for (int i = 0; i < n; i++) {
    a[i] = read();
    mp[a[i]]++;
  }
  sort(a, a + n);
  int ans = 0;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (i == j) continue;
      if (used[{a[i], a[j]}]) continue;
      used[{a[i], a[j]}] = 1;
      mp[a[i]]--, mp[a[j]]--;
      ans = max(check(a[i], a[j]), ans);
      mp[a[i]]++, mp[a[j]]++;
    }
  }
  cout << ans + 2 << endl;
  return 0;
}
