Problem Statement

We have $N$ integers. The $i$-th integer is $A_i$.

Find $\sum_{i=1}^{N-1}\sum_{j=i+1}^{N} (A_i \text{ XOR } A_j)$, modulo $(10^9+7)$.

What is $\text{ XOR }$? The XOR of integers $A$ and $B$, $A \text{ XOR } B$, is defined as follows: When $A \text{ XOR } B$ is written in base two, the digit in the $2^k$'s place ($k \geq 0$) is $1$ if either $A$ or $B$, but not both, has $1$ in the $2^k$'s place, and $0$ otherwise. For example, $3 \text{ XOR } 5 = 6$. (In base two: $011 \text{ XOR } 101 = 110$.)

Constraints

• $2 \leq N \leq 3 \times 10^5$
• $0 \leq A_i < 2^{60}$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the value $\sum_{i=1}^{N-1}\sum_{j=i+1}^{N} (A_i \text{ XOR } A_j)$, modulo $(10^9+7)$.