Problem Statement

You are given an integer sequence of length $N$, $A=(A_1, A_2, \cdots, A_N)$. Snuke wants to make $A$ a non-decreasing sequence.

He can perform the following operation zero or more times.

• Choose two adjacent elements of $A$
• Remove these two elements and insert the bitwise $\mathrm{OR}$ of these two values at the original position

Find the maximum possible value of the length of $A$ when $A$ becomes a non-decreasing sequence.

What is bitwise $\mathrm{OR}$? The bitwise $\mathrm{OR}$ of non-negative integers $A$ and $B$, $A\ \mathrm{OR}\ B$, is defined as follows. When $A\ \mathrm{OR}\ B$ is written in binary, the digit in the $2^k$ place ($k \geq 0$) is $1$ if at least one of the digits in the $2^k$ place of $A$ and $B$ written in binary is $1$, and $0$ otherwise. For example, $3\ \mathrm{OR}\ 5 = 7$ (in binary: $011\ \mathrm{OR}\ 101 = 111$).

What is a non-decreasing sequence? A sequence $a=(a_1,a_2, \cdots, a_n)$ is a non-decreasing sequence if and only if $a_1 \le a_2 \le \ldots \le a_n$ holds.

Constraints

• $1 \le N \le 2 \times 10^5$
• $1 \le A_i <2^{30}$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N
A_1 A_2 \ldots A_N

Output

Print the answer.