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<cstdio>
#include<cmath>
#include<cstring>
#include<algorithm>
#include<queue>
#include<map>
#include<vector>
#include<functional>
#include <random>
#include<iostream>
using namespace std;

long long N;
long long C[200000];
long long pow2[200001];


long long mod_prod(long long a, long long b) {
	return (a*b) % 1000000007;
}

int main() {
	cin >> N;
	for (int i = 0; i < N; i++) {
		cin >> C[i];
	}
	pow2[0] = 1;
	for (int i = 1; i < 200002; i++) {
		pow2[i] = mod_prod(pow2[i - 1], 2) ;
	}

	sort(C, C + N);

	long long ans = 0;
	for (int i = 0; i < N; i++) {
		ans += mod_prod(C[N-i-1], (pow2[N-1] + mod_prod(i, pow2[N - 2])));
		ans = ans % 1000000007;
	}
	ans = mod_prod(ans, pow2[N]);
	cout << ans;
}