Given an array $A$ with $N$ non-negative integers $a_i$ $(1\le i\le N)$, find the longest subsequence $B$, where $b_i\mathrm{\&}{b}_{i-1}$ is not $0$.

NOTE: $\mathrm{\&}$ is the bitwise and operation. A subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements. The two adjacent elements in the subsequence $B$ don't have to be consecutive in the original array $A$.

Input Specification

The first line consists of one integer $N$ $(1\le N\le 100000)$.

The second line consists of $N$ non-negative integers, $a_i$ $(0\le a_i\le {10}^9)$.

Output Specification

One integer, the longest length of the subsequence $B$.

Sample Input 1

4
1 2 3 4

Sample Output 1

2

Sample Input 2

8
1 2 1 2 1 2 1 4

Sample Output 2

4