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.Generic;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;
using static System.Console;
using static System.Math;
using static MyIO;
using static MyUtil;

public class E
{
	public static void Main() => (new Solver()).Solve();
}

public class Solver
{
	public void Solve()
	{
		long N = GetLong();
		long[] C = GetLongs((int)N);
		Array.Sort(C);

		var ans = new ModInt(0);
		for(long i = 0; i < N; i++)
		{
			long l = i;
			long r = N - i - 1;
			var tmp = ModInt.modPow(new ModInt(2), new ModInt(r));
			if(r > 0)
				tmp += ModInt.modPow(new ModInt(2), new ModInt(r - 1)) * r;

			ans += tmp * ModInt.modPow(new ModInt(2), new ModInt(l)) * C[i];
		}
		ans *= ModInt.modPow(new ModInt(2), new ModInt(N));

		WriteLine(ans.Val);
	}
}

public struct ModInt
{
	public long Mod { get; private set; }
	public long Val { get; private set; }

	public ModInt(long v)
	{
		// must initialize (default: Mod = 0)
		Mod = 1000000007;
		Val = (v + Mod) % Mod;
	}

	public static ModInt operator+(ModInt x, ModInt y)
	{
		long mod = x.Mod;
		long tmp = x.Val + y.Val;
		if(tmp >= mod)
			tmp -= mod;
		return new ModInt(tmp);
	}

	public static ModInt operator-(ModInt x, ModInt y)
	{
		long mod = x.Mod;
		long tmp = x.Val;
		if(tmp < y.Val)
			tmp += mod;
		tmp -= y.Val;
		return new ModInt(tmp);
	}

	public static ModInt operator*(ModInt x, ModInt y)
	{
		long mod = x.Mod;
		return new ModInt((x.Val * y.Val) % mod);
	}

	public static ModInt operator/(ModInt x, ModInt y)
	{
		long mod = x.Mod;
		long pow = mod - 2;
		long yy = y.Val;
		long inv = 1;
		while(pow > 0)
		{
			if((pow & 1) == 1)
				inv = (inv * yy) % mod;
			yy = (yy * yy) % mod;
			pow >>= 1;
		}
		return new ModInt((x.Val * inv) % mod);
	}

	public static ModInt modPow(ModInt x, ModInt y)
	{
		long mod = x.Mod;
		long xx = x.Val;
		long exp = y.Val;
		long res = 1;
		while(exp > 0)
		{
			if((exp & 1) == 1)
				res = (res * xx) % mod;

			xx = (xx * xx) % mod;
			exp >>= 1;
		}
		return new ModInt(res);
	}

	public static ModInt operator+(ModInt x, long y) => x + new ModInt(y);
	public static ModInt operator-(ModInt x, long y) => x - new ModInt(y);
	public static ModInt operator*(ModInt x, long y) => x * new ModInt(y);
	public static ModInt operator/(ModInt x, long y) => x / new ModInt(y);
	public static ModInt operator++(ModInt x) => x + new ModInt(1);
	public static ModInt operator--(ModInt x) => x - new ModInt(1);
}

public static class MyIO
{
	private static string[] args = null;
	private static int num = -1;
	private static int used = -1;

	private static string getArg()
	{
		if(used == num)
		{
			args = Console.ReadLine().Split(' ');
			num = args.Length;
			used = 0;
		}
		return args[used++];
	}

	public static int GetInt() => int.Parse(getArg());
	public static long GetLong() => long.Parse(getArg());
	public static double GetDouble() => double.Parse(getArg());
	public static decimal GetDecimal() => decimal.Parse(getArg());
	public static string GetString() => getArg();
	public static char GetChar() => getArg()[0];
	public static int[] GetInts(long N) => Enumerable.Range(0, (int)N).Select(_ => GetInt()).ToArray();
	public static long[] GetLongs(long N) => Enumerable.Range(0, (int)N).Select(_ => GetLong()).ToArray();
	public static double[] GetDoubles(long N) => Enumerable.Range(0, (int)N).Select(_ => GetDouble()).ToArray();
	public static decimal[] GetDecimals(long N) => Enumerable.Range(0, (int)N).Select(_ => GetDecimal()).ToArray();
	public static string[] GetStrings(long N) => Enumerable.Range(0, (int)N).Select(_ => GetString()).ToArray();
}

public static class MyUtil
{
	public static void chmax<T>(ref T x, T y) where T : IComparable<T>
	{
		if(x.CompareTo(y) < 0)
			x = y;
	}

	public static void chmin<T>(ref T x, T y) where T : IComparable<T>
	{
		if(x.CompareTo(y) > 0)
			x = y;
	}

	public static void swap<T>(ref T x, ref T y)
	{
		T tmp = x;
		x = y;
		y = tmp;
	}
}