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: Runtime Error)

using System;
using System.Linq;

class Program
{
	static void Main(string[] args)
	{
		// 入力
        var n = int.Parse(Console.ReadLine());
		string[] input = Console.ReadLine().Split(' ');
        double x = Math.Pow(10, 9) +7;

        //数値に変換
        long[] tmp = new long[n];
        for (int i = 0; i < n; i++)
        {
            tmp[i] = long.Parse(input[i]);
        }

        //XOR(排他的論理和)を取得
        long[,] b = new long[n,n];
        for (int i = 0; i < n; i++)
        {
            for (int k = i+1; k < n; k++)
            {
                b[i,k] = tmp[i] ^ tmp[k];
            }
        }

        double count = 0;
        for (int i = 0; i < n; i++)
        {
            for (int k = 0; k < n; k++)
            {
                count += b[i,k];
            }
            
        }

        //出力
        Console.WriteLine(count%x);
	}
}