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 <bits/stdc++.h>
#define pb push_back
#define mp make_pair
#define int long long
#define inf 1000000007
#define LINF 100000000000000007LL
#define ll long long
using namespace std;
int modpow(int x,int k){
	// x ^ k mod inf
	int res = 1;
	while(k>0){
		if(k%2)res = (res*x)%inf;
		x = (x*x)%inf;
		k >>=1;
	}
	return res;
}
signed main(){
	int n;
	cin>>n;
	vector<int> c(n);
	for(int i=0;i<n;i++){
		cin>>c[i];
	}
	sort( c.begin(), c.end() );
	int ans = 0;
	for(int i=0;i<n;i++){
		int res = 1;
		int nokori = n-1-i;
		res *= modpow( 2, 2*n-2 );
		res *= nokori + 2;
		res %= inf;
		res *= c[i];
		res %= inf;
		ans += res;
		ans %= inf;
	}
	cout<<ans<<endl;
	return 0;
}