A9195 | The Fibonacci Segment

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.

The first line contains a single integer $n$ ( $1<=n<=10^{5}$ ) — the number of elements in the array. The second line contains integers: $a_{1},a_{2},...,a_{n}$ ( $0<=a_{i}<=10^{9}$ ).

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