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
/* 
* ID: juryc
* PROG: Change a little bit
* LANG: C++
*/
#include<bits/stdc++.h>
using namespace std;
const int N = 2*1e5+5;
typedef long long ll;
ll n; 
ll mod=1e9+7;
ll v[N]; 
ll modpow(ll a,ll b){
ll res=1;a%=mod;
while(b){
if(b&1){res=(res*a)%mod; }
a=(a*a)%mod;
b>>=1;
}
return res;
}
int main(){
cin>>n;
for(int i=1;i<=n;i++) cin>>v[i];
sort(v+1,v+1+n); 
ll ans=modpow(2,2*n-2),sum=0; 
for(ll i=1;i<=n;i++){
sum=(sum+((n-i+2)*v[i])%mod)%mod;
}
cout<<(ans*sum)%mod<<"\n"; 
return 0;
} 

