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# (.NET Core 3.1.201) (judge verdict: Time Limit Exceeded)

using System;
using System.Security.Cryptography;

namespace D
{
    class Program
    {
        static public readonly uint Mod = 1000000007;
        static void Main(string[] args)
        {
            uint n = uint.Parse(Console.ReadLine());
            ulong[] A = new ulong[n+1];
            string[] In = Console.ReadLine().Split(' ');
            for(uint i=0; i < n; i++)
            {
                A[i+1] = ulong.Parse(In[i]);
            }
            ulong sum = 0;
            for(uint i = 1; i <= n - 1; i++)
            {
                for(uint j=i+1; j <= n; j++)
                {
                    ulong temp = A[i] ^ A[j];                    
                    sum +=(temp % Mod);
                    sum %= Mod;
                }
            }
            Console.WriteLine(sum);
        }

    }
}