Given an array A of length N . Find the length of longest subarray which forms an arithmetic progression  . 

For example if the array is \([3,5,2,4,6,9]\) then subarray \([2,4,6]\)  forms an  A.P. with common difference 2 having maximum length 3 .

INPUT

First line of input contains one integer N number of elements in array.

Second line contains N elements  .

OUTPUT

Print the length of longest arithmetic subarray .

CONSTRAINTS

\(2 \leq N \leq 10^{6}\)

\(-10^{6} \leq A[i] \leq 10^{6}\)