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.Arrays;
import java.util.Scanner;

public class Main {

	private static final long M = 1_000_000_007;

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		long[] c = new long[n];
		for (int i = 0; i < n; i++) {
			c[i] = sc.nextLong();
		}
		Arrays.sort(c);
		long[] t = new long[n + 1];
		t[0] = 1;
		for (int i = 1; i <= n; i++) {
			t[i] = t[i - 1] * 2;
			t[i] %= M;
		}

		long answer = 0;
		for (int i = 0; i < n; i++) {
			int l = i, r = n - 1 - i;
			long a = t[r];
			if (r != 0) a = (a + (t[r - 1] * r)) % M;
			a = a * t[l] % M;
			a = a * c[i] % M;

			answer += a;
			answer %= M;
		}
		answer *= t[n];
		System.out.println(answer % M);
	}
}
