Longest Interesting Subsequence

Problem Description

A sequence is called interesting if and only if the bitwise AND of every two adjacent elements is non-zero.

That is, for a sequence $\{a\}$ of length $n$, it satisfies $\forall x < n,\ a[x]\ \&\ a[x+1] \neq 0$.

Given a sequence $\{a\}$ of length $n$, what is the length of the longest interesting subsequence?

Input Format

One line containing an integer $1\le n \le 10^6$.

The next line contains $n$ integers $1 \le a_i \le 2^{31} - 1$.

Output Format

One line containing an integer: the length of the longest interesting subsequence.

Sample Input

3
1 2 3

Sample Output

2