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.
n = int(input())
a = [int(i) for i in input().split()]
ans = a.count(0)
d, s = dict(), set(a)
for i in a:
    if i not in d.keys():
        d[i] = 0
    d[i] += 1
for i in range(n):
    for j in range(n):
        if i == j or a[i] == a[j] == 0: continue
        a1, a2 = a[i], a[j]
        ln, dl = 2, [a1, a2]
        d[a1] -= 1
        d[a2] -= 1
        while a1 + a2 in s:
            a1, a2 = a2, a1 + a2
            d[a2] -= 1
            dl.append(a2)
            if d[a2] < 0:
                break
            ln += 1
        ans = max(ans, ln)
        for v in dl:
            d[v] += 1
print(ans)
