Codeforces 633D Fibonacci-ish 【暴力递归】

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.

定义 K数列：f[0]、f[1]任意，对于n > 1，f[n] = f[n-1] + f[n-2]。

题意：给定n个元素，构造最长的K数列。

思路：以为暴力枚举会T。。。记录元素个数并去重，递归构造。

AC代码：

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