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;

int MOD = 1e9 + 7;
int n;
long long ans, a[500000];
long long deg[500000];
long long k[500000];

int main()
{
	cin >> n;
	for (int i = 0; i < n; i++) cin >> a[i];
	sort(a, a + n);
	int r = 1;
	for (int i = 0; i < n; i++) deg[i] = r, r = 2 * r % MOD;
	deg[n] = r;
	for (int i = 0; i < n; i++) a[i] = a[i] * r % MOD;
	k[0] = 1;
	for (int i = 1; i < n; i++)
	{
		k[i] = (k[i - 1] * 2 + deg[i - 1]) % MOD;
	}
	for (int i = 0; i < n; i++)
	{
		ans = (ans + a[i] * deg[i] % MOD * k[n - i - 1]) % MOD;
	}
	cout << ans;
}