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(raw_input())
arr=list(map(int,raw_input().split()))
dic={}
for i in arr:
    dic[i]=dic.get(i,0)+1
ans=1
for i in range(n):
    for j in range(n):
        if i!=j:
            if arr[i]==arr[j]==0:
                ans=max(ans,dic[0])
            else:
                a,b=arr[i],arr[j]
                dic[a]-=1
                ln=1
                while(dic.get(b,0)):
                    dic[b]-=1
                    a,b=b,a+b
                    ln+=1
                ans=max(ans,ln)
                while(ln>0):
                    dic[a]+=1
                    a,b=b-a,a
                    ln-=1
print(ans)