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.Collections.Generic;
using System.Linq;

namespace xor
{
    class Program
    {
        static void Main(string[] args)
        {
            var count = int.Parse(Console.ReadLine());

            var nums = Console.ReadLine().Split(' ').Select(c => long.Parse(c)).ToList();

            var sum = EnumerateCombination(nums.Select((n,i) => new Num(n, i)), 2)
                        .Select(c => c[0].Value ^ c[1].Value)
                        .Sum();

            var x = Math.Pow(10, 9) + 7;
            Console.WriteLine(sum % x);
        }

        class Num
        {
            public long Value { get; }
            public int Idx { get; }

            public Num(long n, int idx)
            {
                this.Value = n;
                this.Idx = idx;
            }
        }

        private static IEnumerable<Num[]> EnumerateCombination(IEnumerable<Num> all, int count)
        {
            if (count == 0)
            {
                yield break;
            }
            if (count == 1)
            {
                foreach (var n in all)
                {
                    yield return new[] { n };
                }
                yield break;
            }

            foreach (var n in all)
            {
                var leftside = new[] { n };

                var unused = all.SkipWhile(e => e.Idx != n.Idx).Skip(1).ToList();

                foreach (var rightside in EnumerateCombination(unused, count - 1))
                {
                    yield return leftside.Concat(rightside).ToArray();
                }
            }
        }
    }
}