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 <cstdlib>
using namespace std;
typedef long long int lli;
lli mod = 1e9 +7;

lli modpow(lli a, lli p){
	lli ret = 1;
	for(int i=63; i>=0; i--){
		ret *= ret;
		ret %= mod;
		if((1LL<<i & p) != 0){
			ret *= a;
			ret %= mod;
		}
	}
	return ret;
}

int main(){
	int n;
	cin >> n;
	vector<lli> a(n);
	for(int i=0; i<n; i++) cin >> a[i];
	sort(a.begin(), a.end(), greater<lli>());

	lli ans = 0;
	int num = modpow(2, n-1);
	for(int i=0; i<n; i++){
		ans += num *a[i];
		ans %= mod;
		num += modpow(2, n-2);
		num %= mod;
	}
	ans *= modpow(2, n);
	ans %= mod;
	cout << ans << endl;
	return 0;
}