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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Arrays;

public class Main {
	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] sa = br.readLine().split(" ");
		int n = Integer.parseInt(sa[0]);
		sa = br.readLine().split(" ");
		int[] c = new int[n];
		for (int i = 0; i < n; i++) {
			c[i] = Integer.parseInt(sa[i]);
		}
		br.close();

		int mod = 1000000007;
		if (n == 1) {
			System.out.println(c[0] * 2 % mod);
			return;
		}

		Arrays.parallelSort(c);
		long b = power(2, n);
		long a = power(2, n - 2);
		long ans = 0;
		for (int i = 2; i <= n + 1; i++) {
			long val = a * i % mod;
			val *= c[n + 1 - i];
			val %= mod;
			ans += val;
			ans %= mod;
		}
		ans *= b;
		ans %= mod;
		System.out.println(ans);
	}

	static long power(long x, long n) {
		if (n == 0) {
			return 1;
		}
		int mod = 1000000007;
		long val = power(x, n / 2);
		val = val * val % mod;
		if (n % 2 == 1) {
			val = val * x % mod;
		}
		return val;
	}
}
