Interesting Sections
Description
William has an array of non-negative numbers $a_1, a_2, \dots, a_n$. He wants you to find out how many segments $l \le r$ pass the check. The check is performed in the following manner:
- The minimum and maximum numbers are found on the segment of the array starting at $l$ and ending at $r$.
- The check is considered to be passed if the binary representation of the minimum and maximum numbers have the same number of bits equal to 1.
The first line contains a single integer $n$ ($1 \le n \le 10^6$), the size of array $a$.
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 10^{18}$), the contents of array $a$.
Output a single number — the total number of segments that passed the check.
Input
The first line contains a single integer $n$ ($1 \le n \le 10^6$), the size of array $a$.
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 10^{18}$), the contents of array $a$.
Output
Output a single number — the total number of segments that passed the check.
Samples
5
1 2 3 4 5
9
10
0 5 7 3 9 10 1 6 13 7
18