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
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;


typedef long long LL;

const LL BASE = 1000000007;


LL pow2(LL M) {
	if (M == 0) return 1LL;

	LL a = M / 2;
	LL b = pow2(a);
	b = (b * b) % BASE;
	if (M % 2) b = (b * 2) % BASE;

	return b;
}


int main() {
	int N;
	cin >> N;

	vector<LL> C(N);
	for (int i = 0; i < N; ++i)
		cin >> C[i];

	sort(C.begin(), C.end());

	LL ans = 0;
	for (int i = 0; i < N; ++i) {
		LL cost = (C[i] * (N - i + 1)) % BASE;
		ans = (ans + cost) % BASE;
	}

	ans = (ans * pow2(2 * N - 2)) % BASE;

	cout << ans << endl;

	return 0;
}
