A12031. Vasya and Good Sequences

Vasya has a sequence $a$ consisting of $n$ integers $a_1, a_2, \dots, a_n$ . Vasya may pefrom the following operation: choose some number from the sequence and swap any pair of bits in its binary representation. For example, Vasya can transform number $6$ $(\dots 00000000110_2)$ into $3$ $(\dots 00000000011_2)$ , $12$ $(\dots 000000001100_2)$ , $1026$ $(\dots 10000000010_2)$ and many others. Vasya can use this operation any (possibly zero) number of times on any number from the sequence.

Vasya names a sequence as good one, if, using operation mentioned above, he can obtain the sequence with [bitwise exclusive or](https://en.wikipedia.org/wiki/Exclusive_or) of all elements equal to $0$ .

For the given sequence $a_1, a_2, \ldots, a_n$ Vasya'd like to calculate number of integer pairs $(l, r)$ such that $1 \le l \le r \le n$ and sequence $a_l, a_{l + 1}, \dots, a_r$ is good.

The first line contains a single integer $n$ ( $1 \le n \le 3 \cdot 10^5$ ) — length of the sequence.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ( $1 \le a_i \le 10^{18}$ ) — the sequence $a$ .

Print one integer — the number of pairs $(l, r)$ such that $1 \le l \le r \le n$ and the sequence $a_l, a_{l + 1}, \dots, a_r$ is good.

In the first example pairs $(2, 3)$ and $(1, 3)$ are valid. Pair $(2, 3)$ is valid since $a_2 = 7 \rightarrow 11$ , $a_3 = 14 \rightarrow 11$ and $11 \oplus 11 = 0$ , where $\oplus$ — bitwise exclusive or. Pair $(1, 3)$ is valid since $a_1 = 6 \rightarrow 3$ , $a_2 = 7 \rightarrow 13$ , $a_3 = 14 \rightarrow 14$ and $3 \oplus 13 \oplus 14 = 0$ .

In the second example pairs $(1, 2)$ , $(2, 3)$ , $(3, 4)$ and $(1, 4)$ are valid.