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)

N = int(input())
A = [int(i) for i in input().split()]
A.sort()
list_A = []
num_A = []
list_A.append(A[0])
j = 1
cnt = 1
while(j<=N-1):
    if A[j-1]==A[j]:
        cnt += 1
        if j == N-1:
            num_A.append(cnt)
    else:
        list_A.append(A[j])
        num_A.append(cnt)
        cnt = 1
        if j == N-1:
            num_A.append(cnt)
    j += 1
len_A = len(list_A)
j = 0
k = 1
xor = 0
while(j<=len_A-2):
    xor += (list_A[j]^list_A[k])*(num_A[j]*num_A[k])
    k += 1
    if k == len_A:
        j += 1
        k = j+1
print(xor%(10**9+7))