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 {
	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] c = new int[n];
		for (int i = 0; i < n; i++) {
			c[i] = sc.nextInt();
		}
		sc.close();

		int mod = 1000000007;
		int m2 = 1000000008 / 2;
		Arrays.sort(c);
		long ans = 0;
		long base = 0;
		long d = 1;
		long time = power(2, n, mod);
		long total = time;
		for (int i = 0; i < n; i++) {
			base = base * 2 + d;
			base %= mod;
			if (i != 0) {
				d *= 2;
				d %= mod;
			}
			time *= m2;
			time %= mod;
			long val = base * time % mod;
			val = val * c[n - 1 - i] % mod * total % mod;
			ans += val;
			ans %= mod;
		}
		System.out.println(ans);
	}

	static long power(long x, long n, int m) {
		if (n == 0) {
			return 1;
		}
		long val = power(x, n / 2, m);
		val = val * val % m;
		if (n % 2 == 1) {
			val = val * x % m;
		}
		return val;
	}
}
