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>
#include <cmath>
#include <functional>
using namespace std;
using uint = unsigned int;
using ull = unsigned long long;

int main() {
	uint N;
	cin >> N;
	
	vector<ull> C(N);
	for(uint i=0; i<N; i++) cin >> C[i];
	
	sort(C.begin(), C.end(), greater<uint>());
	
	ull mod = pow(10, 9) + 7;
	ull ans = 0;
	
	for(uint i=0; i<N; i++) {
		ull tans = C[i] * (i + 2) % mod;
		ans = (ans + tans) % mod;
	}
	
	for(uint i=1; i<N; i++) {
		ans = (ans * 4) % mod;
	}
	
	cout << ans;
	
	return 0;
}
