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())
l = list(map(int,input().split()))
d = {}
for i in l:
	if i not in d: d[i] = 0
	d[i] += 1
ans = 0
for i in range(len(l)):
	for j in range(len(l)):
		if i==j: continue		
		n1,n2 = l[i],l[j]
		if n1==0 and n2==0: continue
		curr = 2
		d2 = {n1:1,n2:1}
		while True:
			n1,n2 = n2,n1+n2
			ans = max(ans, curr)
			if n2 in d and (d2[n2] if n2 in d2 else 0) < d[n2]:
				if n2 not in d2: d2[n2] = 0
				d2[n2] += 1
				curr += 1
			else: break
print(max(ans, (d[0] if 0 in d else -1)))
