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.
def main():
    from collections import Counter
    n = int(input())
    cnt, res = dict(Counter(map(int, input().split()))), []
    x = cnt.get(0, 0)
    if x * 2 >= n:
        print(cnt[0])
        return
    cget, rpush = cnt.get, res.append
    if x:
        rpush(x)
        cnt[0] = 1

    def deeper(a, b, lvl):
        if cget(a + b, 0):
            c = a + b
            cnt[c] -= 1
            deeper(b, c, lvl + 1)
            cnt[c] += 1
        else:
            rpush(lvl)

    for x in cnt:
        cnt[x] -= 1
        for y in cnt:
            if cnt[y]:
                cnt[y] -= 1
                deeper(x, y, 2)
                cnt[y] += 1
        cnt[x] += 1
    print(max(res))


if __name__ == '__main__':
    main()
