As an experiment the Educational Codeforces Round 33 will be rated for Div. 2. ×

D. Fibonacci-ish
time limit per test
3 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

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 , , , , 28.