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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;


public class A
{
    static long mod = 1000000007;
    static long sumXOR(long[] arr, int n)
    {
        long sum = 0;
        for (int i = 0; i < 64; i++)
        {
            // Count of zeros and ones 
            long zc = 0, oc = 0;

            // Individual sum at each bit position 
            long idsum = 0;

            for (int j = 0; j < n; j++)
            {
                if (arr[j] % 2 == 0)
                    zc++;

                else
                    oc++;
                arr[j] /= 2;
            }

            // calculating individual bit sum  
            idsum = (((long)1 << i) % mod);
            idsum =  (idsum * zc) % mod ;
            idsum = (idsum * oc) % mod;

            // final sum  
            sum = (sum + idsum) % mod;
        }
        return sum;
    }
    public static void Main(string[] args)
    {
        int t = 1;
        while (t > 0)
        {
            int n = int.Parse(Console.ReadLine());
            var arr = Console.ReadLine().Trim().Split().Select(x => long.Parse(x)).ToArray();
            
            
            Console.WriteLine(sumXOR(arr,n));
            t--;
        }
    }
}