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>
using namespace std;
typedef long long ll;
#define For(i,n,k) for(ll i=(n);i<(k);i++)
#define ALL(a)  (a).begin(),(a).end()
ll ans=0;
const ll MOD = 1000000007;
void Main(){
    ll n;cin>>n;
    vector<ll> c(n);
    For(i,0,n) cin>>c[i];
    sort(ALL(c));
    reverse(ALL(c));
    ll N4=1;
    For(i,0,n-1) N4=N4*4%MOD;
    For(i,0,n){
         ans+=(i+2)*c[i]%MOD;
         ans%=MOD;
    }
    ans*=N4;
    ans%=MOD;
    cout<<ans<<endl;
}
int main(){
     Main();
     return 0;
}