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.
import sys
sys.setrecursionlimit(10000)
n = int(input())
a = list(map(int, input().split()))

# sa = dict(zip(a, range(n)))
sb = {}
for num in a:
    if not num in sb:
        sb[num]=1
    else:
        sb[num]+=1

def go(a, b):
    ans = 0
    ab = a+b
    if ab in sb and sb[ab]>0:
        sb[ab]-=1
        ans = 1 + go(b, ab)
        sb[ab]+=1
    return ans

maxans = 2
for a in sb:
    for b in sb:
        if a!=b or sb[a]>1:
            count = 2
            sb[a] -= 1
            sb[b] -= 1
            count += go(a,b)
            sb[a] += 1
            sb[b] += 1
            if count > maxans:
                maxans = count
print(maxans)