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;
using System.Collections.Generic;
using System.Numerics;
using System.Linq;

namespace c
{
    class Program
    {
        public static readonly long INF = 999999999999;
        public static readonly long MOD = 1000000007;

        static void Main(string[] args)
        {
            var n = Scanner.LongScan()[0];
            var a = Scanner.LongScan();
            var res = 0.0;
            for(var i = 0; i < n - 1; i++)
            {
                for(var j = i + 1; j < n; j++)
                {
                    res += a[i] ^ a[j];
                    res %= MOD;
                }
            }
            Console.WriteLine(res);
        }
    }

    public class Scanner
    {
        public static string[] Scan() => Console.ReadLine().Split(' ');
        public static int[] IntScan() => Array.ConvertAll(Scan(), int.Parse);
        public static long[] LongScan() => Array.ConvertAll(Scan(), long.Parse);
        public static string[][] Scan(int n) => Enumerable.Repeat(0, n).Select(_ => Scan()).ToArray();
        public static int[][] IntScan(int n) => Enumerable.Repeat(0, n).Select(_ => IntScan()).ToArray();
        public static long[][] LongScan(int n) => Enumerable.Repeat(0, n).Select(_ => LongScan()).ToArray();

    }

    public class Ex
    {
        public static bool Chmin(ref int a, int b) { if (a > b) { a = b; return true; } return false; }
        public static bool Chmin(ref long a, long b) { if (a > b) { a = b; return true; } return false; }
        public static bool Chmax(ref int a, int b) { if (a < b) { a = b; return true; } return false; }
        public static bool Chmax(ref long a, long b) { if (a < b) { a = b; return true; } return false; }
        public static int[] SubArr(int[] arr, int begin, int n) { int[] a = new int[arr.Length]; Array.Copy(arr, begin, a, 0, n); return a; }
    }
}