Yash has recently learnt about the Fibonacci sequence and is very excited about it. He calls a sequence Fibonacci-ish if
-
the sequence consists of at least two elements
-
f0 and f1 are arbitrary
-
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.
Output
Print the length of the longest possible Fibonacci-ish prefix of the given sequence after rearrangement.
Yash最近迷上了fibonacci数列,他定义了一种数列叫fibonacccccci数列: 1. 这个数列包含至少2个元素; 2. f[0]和f[1]是任意选取的; 3. f[n+2]=f[n+1]+f[n] (n>=0); 现在,给出一个数列a[1..n],你可以改变数列元素的顺序,使得a[1..m] 满足fibonacccccci数列的条件,请求出最大的m。
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.