# Circle of Friends

There is a posse of friends sitting in a circle. Each friend is holding a card containing a positive integer.

You would like to split the circle of friends into one or
more groups. Each group must be a contiguous subsection of the
circle. In addition, for each group, the bitwise *AND*
of all values on the cards of the members of the group, taken
together, must be nonzero.

Count the number of ways you could split the circle of friends into groups.

## Input

The first line of input contains a single integer $n$ ($1 \leq n \leq 2 \cdot 10^5$), which is the number of friends in the circle.

Each of the next $n$ lines contains a single integer $a$ ($1 \le a < 2^{60}$). These are the positive integers on the cards held by the friends in the circle, in the order that the friends are sitting. Note that since they’re in a circle, the last friend in the list is sitting next to the first friend in the list.

## Output

Output a single integer, which is the number of ways to split the circle of friends into groups. Since this number may be very large, output it modulo $998\, 244\, 353$.

Sample Input 1 | Sample Output 1 |
---|---|

4 14 13 11 7 |
11 |