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).

Examples

Input

1
1000000000


Output

999999993


Input

2
5 8


Output

124


Input

5
52 67 72 25 79


Output

269312
import java.util.*;

class Main {
	Scanner sc;
	int N;
	int[] C;
	static final int MOD = 1000_000_007;
	
	private void calc() {
		sc = new Scanner(System.in);
		N = sc.nextInt();
		C = new int[N];
		for (int i = 0; i < N; i++) C[i] = sc.nextInt();
		Arrays.sort(C);
		long p = 1;
		for (int i = 0; i < N-1; i++) p = p * 2 % MOD;
		long pp = p * 2 % MOD;
		
		long a = p;
		long sum = 0;
		long d = (p%2==0)?p/2:(p+MOD)/2%MOD;
		for (int i = 0; i < N; i++) {
			sum = (a*C[N-1-i]%MOD + sum)%MOD;
			a = (a + d)%MOD;
		}
		sum = sum * pp % MOD;
		
		System.out.println(sum);
	}
	
	public static void main(String[] args) {
		new Main().calc();
	}
}
