Problem:
Score : 400 points

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 \mbox{ XOR } A_j), modulo (10^9+7).

What is \mbox{ XOR }?

The XOR of integers A and B, A \mbox{ XOR } B, is defined as follows:

When A \mbox{ 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 \mbox{ XOR } 5 = 6. (In base two: 011 \mbox{ 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 \mbox{ XOR } A_j), modulo (10^9+7).

Sample Input 1

3
1 2 3

Sample Output 1

6

We have (1\mbox{ XOR } 2)+(1\mbox{ XOR } 3)+(2\mbox{ 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).

Solution in PyPy3 (2.4.0) (judge verdict: Runtime Error)

import numpy as np
n = int(input())
mod = 10 ** 9 + 7
a = [list(bin(int(i))[2:].zfill(60)) for i in input().split()]
a = np.array(a)
x = a.T
x = x.tolist()
#print(x)
ans = 0
for i in range(60):
    y = x[i].count('0')
    z = x[i].count('1')
    tmp = ( (n * (n - 1) // 2) - (y * (y - 1) // 2) - (z * (z - 1) // 2) ) % mod
    tmp2 = 1
    for j in range(60 - i - 1):
        tmp2 = tmp2 * 2 % mod
    #print(tmp,tmp2)
    
    ans = (ans + tmp2 * tmp) % mod
print(ans)