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: Wrong Answer)

using System;

    class Program
    {
        static void Main(string[] args)
        {
            var n = Console.ReadLine();
            var input = Console.ReadLine().Split(' ');

        int i = 0;

        long sum = 0;
        for(i = 0; i < input.Length -1; i++)
        {
            for (int q = i + 1; q <= input.Length - 1; q++)
            {
                var x2 = Convert.ToString(Int64.Parse(input[i]), 2);
                var y2 = Convert.ToString(Int64.Parse(input[q]), 2);
                var len = x2.Length > y2.Length ? x2.Length : y2.Length;

                var zero = "";
                for (int j = 1; j <= len; j++) zero += "0";
                var x20 = (zero + x2);
                x20 = x20.Substring(x20.Length - len, len);
                var y20 = (zero + y2);
                y20 = y20.Substring(y20.Length - len, len);

                var z = "";
                for (int k = 0; k < len; k++)
                {
                    z += x20[k] != y20[k] ? "1" : "0";
                }

                var z10 = Convert.ToInt64(z, 2);
                sum += z10;
            }

        }
        Console.Write(sum / 1000000007);

    }
}