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#F1336. Fibonacci-ish

    ID: 1342 传统题 2000ms 256MiB 尝试: 0 已通过: 0 难度: 6 上传者: 标签>枚举动态规划哈希模拟数学算法思想数据结构编程与模拟提高难度共享题库Codeforces英文题面题目来源题面语言

Fibonacci-ish

题目描述

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.

题目来源：fps-www.educg.net-codeforce-1-2833.xml.zip；FPS 共享题包，题包内第 834 题。保留原作者与原赛事署名。