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;
typedef long long int ll;

ll mod=1e9+7;

ll mod_pow(ll a,ll b){
	a%=mod;
	if(b==0)return 1;
	if(b==1)return a;
	ll res=mod_pow(a,b/2)%mod;
	res*=res; res%=mod;
	if(b%2)res*=a;
	return res%mod;
}

int main(){
	int n; cin >> n;
	vector<ll> a(n);
	for(int i=0;i<n;i++){
		cin >> a[i];
	}
	ll ans=0;
	sort(a.rbegin(),a.rend());
	for(int i=0;i<n;i++){
		(ans+=mod_pow(4,n-1)*a[i]%mod*(i+2))%=mod;
	}
	cout << ans << endl;
}