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

NOTE: ~\&~ 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 100\,000)~.

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