You have array a1,a2,...,an. Segment [l,r] (1≤l≤r≤n) is good if ai=ai-1+ai-2, for all i(l+2≤i≤r).
Let's define len([l,r])=r-l+1, len([l,r]) is the length of the segment [l,r]. Segment [l1,r1], is longer than segment [l2,r2], if len([l1,r1])>len([l2,r2]).
Your task is to find a good segment of the maximum length in array a. Note that a segment of length 1 or 2 is always good.
Input
The first line contains a single integer n (1≤n≤105) − the number of elements in the array. The second line contains integers: a1,a2,...,an (0≤ai≤109).
Output
Print the length of the longest good segment in array a.