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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

import itertools

N = int(input())
A = list( map(int, input().split()) )

maxA = max(A)
bmaxA = format(maxA, 'b')
n_bmaxA = len(bmaxA)


cmb = itertools.combinations(A, 2)

ans = 0
for item in cmb:

    bfirst = format(item[0], '0{}b'.format(n_bmaxA))
    blast = format(item[1], '0{}b'.format(n_bmaxA))

    cXOR = []
    for i in range(len(bfirst)):
        if bfirst[i] == blast[i]:
            cXOR.append("0")
        else:
            cXOR.append("1")

    cXOR = ''.join(cXOR)
    ans += int(cXOR, 2)


base = 1000000000 + 7
print(ans % base)