Problem:
Score : 500 points

Problem Statement

For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:

Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.

Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.

There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).

Constraints

1 \leq N \leq 2 \times 10^5

1 \leq C_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
C_1 C_2 \cdots C_N

Output

Print the sum of f(S, T), modulo (10^9+7).

Sample Input 1

1
1000000000

Sample Output 1

999999993

There are two pairs (S, T) of different sequences of length 2 consisting of 0 and 1, as follows:

S = (0), T = (1): by changing S_1 to 1, we can have S = T at the cost of 1000000000, so f(S, T) = 1000000000.

S = (1), T = (0): by changing S_1 to 0, we can have S = T at the cost of 1000000000, so f(S, T) = 1000000000.

The sum of these is 2000000000, and we should print it modulo (10^9+7), that is, 999999993.

Sample Input 2

2
5 8

Sample Output 2

124

There are 12 pairs (S, T) of different sequences of length 3 consisting of 0 and 1, which include:

S = (0, 1), T = (1, 0)

In this case, if we first change S_1 to 1 then change S_2 to 0, the total cost is 5 \times 2 + 8 = 18. We cannot have S = T at a smaller cost, so f(S, T) = 18.

Sample Input 3

5
52 67 72 25 79

Sample Output 3

269312

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static System.Math;
using MethodImplAttribute = System.Runtime.CompilerServices.MethodImplAttribute;
using MethodImplOptions = System.Runtime.CompilerServices.MethodImplOptions;

public static class P
{
    public static void Main()
    {
        var n = int.Parse(Console.ReadLine());
        var c = Console.ReadLine().Split().Select(int.Parse).OrderByDescending(x => x).ToArray();
        ModInt res = 0;
        for (int i = 0; i < c.Length; i++)
        {
            res += (((ModInt)i + 2) / 2) * c[i];
        }
        res *= Power(2, 2 * n - 1);
        Console.WriteLine(res);
    }


    static ModInt Power(ModInt n, long m)
    {
        ModInt pow = n;
        ModInt res = 1;
        while (m > 0)
        {
            if ((m & 1) == 1) res *= pow;
            pow *= pow;
            m >>= 1;
        }
        return res;
    }
}


struct ModInt
{
    const int MOD = 1000000007;
    const long POSITIVIZER = ((long)MOD) << 31;
    long Data;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public ModInt(long data) { if ((Data = data % MOD) < 0) Data += MOD; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static implicit operator long(ModInt modInt) => modInt.Data;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static implicit operator ModInt(long val) => new ModInt(val);
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator +(ModInt a, int b) => new ModInt() { Data = (a.Data + b + POSITIVIZER) % MOD };
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator +(ModInt a, long b) => new ModInt(a.Data + b);
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator +(ModInt a, ModInt b) { long res = a.Data + b.Data; return new ModInt() { Data = res >= MOD ? res - MOD : res }; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator -(ModInt a, int b) => new ModInt() { Data = (a.Data - b + POSITIVIZER) % MOD };
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator -(ModInt a, long b) => new ModInt(a.Data - b);
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator -(ModInt a, ModInt b) { long res = a.Data - b.Data; return new ModInt() { Data = res < 0 ? res + MOD : res }; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator *(ModInt a, int b) => new ModInt(a.Data * b);
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator *(ModInt a, long b) => a * new ModInt(b);
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator *(ModInt a, ModInt b) => new ModInt() { Data = a.Data * b.Data % MOD };
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator /(ModInt a, ModInt b) => new ModInt() { Data = a.Data * GetInverse(b) % MOD };
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public override string ToString() => Data.ToString();
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    static long GetInverse(long a)
    {
        long div, p = MOD, x1 = 1, y1 = 0, x2 = 0, y2 = 1;
        while (true)
        {
            if (p == 1) return x2 + MOD; div = a / p; x1 -= x2 * div; y1 -= y2 * div; a %= p;
            if (a == 1) return x1 + MOD; div = p / a; x2 -= x1 * div; y2 -= y1 * div; p %= a;
        }
    }
}