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 copy import * 
length=int(input())
arr=list(map(int,input().split()))
d=dict()
for i in arr:
    d[i]=d.get(i,0)+1
ans=0
for i in range(len(arr)):
    for j in range(len(arr)):
        if i!=j:
            if arr[i]==0 and arr[j]==0:
                ans=max(ans,d[arr[i]])
            else:
                count=2
                a=arr[i]
                b=arr[j]
                d[a]-=1 
                d[b]-=1 
                for k in range(100):
                    if d.get(a+b):
                        count+=1 
                        d[a+b]-=1 
                        c=a+b
                        a=b
                        b=c
                    else:
                        d[a]+=1 
                        d[b]+=1
                        ans=max(ans,count)
                        break
                y=count-2 
                while y>0:
                    c=b-a 
                    d[c]=d.get(c,0)+1 
                    b=a 
                    a=c 
                    y-=1 
print(ans)
            