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 shu[1008];
int he[1008][1008];
int len[1008][1008];
int used[1008];
map<int, int> mapa;
int n;
int hehe;
int getdp(int i, int j) {
  if (used[j] == 0) return 1;
  if (he[i][j] == -1) return 2;
  used[j]--;
  int t = getdp(j, he[i][j]) + 1;
  used[j]++;
  return t;
}
int main() {
  int t;
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    scanf("%d", &t);
    if (mapa.find(t) == mapa.end()) {
      mapa.insert({t, i});
      shu[i] = t;
      used[i] = 1;
    } else {
      i--;
      n--;
      used[mapa[t]]++;
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      hehe = shu[i] + shu[j];
      if (mapa.find(hehe) != mapa.end()) {
        he[i][j] = mapa[hehe];
        he[j][i] = mapa[hehe];
      } else {
        he[i][j] = -1;
        he[j][i] = -1;
      }
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (j == i && used[i] == 1) continue;
      used[i]--;
      len[i][j] = getdp(i, j);
      used[i]++;
    }
  }
  int maxl = 0;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (len[i][j] > maxl) {
        maxl = len[i][j];
      }
    }
  }
  cout << maxl << endl;
  return 0;
}
