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.
from collections import defaultdict

n = int(raw_input())
arr = map(int, raw_input().split())
dd = defaultdict(int)
for i in arr:
	dd[i] += 1
out = 0
for i in xrange(n):
	for j in xrange(n):
		if i == j:
			continue
		a = arr[i]
		b = arr[j]
		c = a + b
		d = 2
		dd[a] -= 1
		dd[b] -= 1
		dl = [a, b]
		while dd[c] > 0:
			if a == 0 and b == 0:
				break
			d += 1
			dd[c] -= 1
			dl.append(c)
			a, b = b, c
			c = a + b
		for item in dl:
			dd[item] += 1
		out = max(out, d)

# yes = 0
# for i in arr:
# 	if i != 0 and -i in dd:
# 		yes = 1
# 		break

# print max(out, arr.count(0) + yes)
print max(out, arr.count(0))
