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 $(10^9+7)$.

Sample Input 1

3
1 2 3

Sample Output 1

6

We have $(1\\text{ XOR } 2)+(1\\text{ XOR } 3)+(2\\text{ XOR } 3)=3+2+1=6$.

Sample Input 2

10
3 1 4 1 5 9 2 6 5 3

Sample Output 2

237

Sample Input 3

10
3 14 159 2653 58979 323846 2643383 27950288 419716939 9375105820

Sample Output 3

103715602

Print the sum modulo $(10^9+7)$.