You have array $*a*_{1}, *a*_{2}, ..., *a*_{*n*}$. Segment $[*l*, *r*]$ ($1 ≤ *l* ≤ *r* ≤ *n*$) is good if $*a*_{*i*} = *a*_{*i* - 1} + *a*_{*i* - 2}$, 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 $[*l*_{1}, *r*_{1}]$, is longer than segment $[*l*_{2}, *r*_{2}]$, if $*len*([*l*_{1}, *r*_{1}]) > *len*([*l*_{2}, *r*_{2}])$.

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 $*n*$ ($1 ≤ *n* ≤ 10^{5}$) — the number of elements in the array. The second line contains integers: $*a*_{1}, *a*_{2}, ..., *a*_{*n*}$ ($0 ≤ *a*_{*i*} ≤ 10^{9}$).

Output

Print the length of the longest good segment in array $*a*$.