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: $011 \text{ XOR } 101 = 110.)$

Input

Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N

Output

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

Constraints

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

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).

见题面 Input 部分

见题面 Output 部分