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;
ll mod = 1e9+7;

int main(void)
{
  ll N;cin>>N;
  vector<ll> C(N);
  for(ll i=0;i<N;i++){
    cin>>C[i];
  }

  sort(C.begin(),C.end());

  ll res = 0;
  ll TC = 0;
  ll TT = 1;
  ll sumC = 0;
  for(ll i=0;i<N;i++){
    ll a1 = TT*TT %mod;
    ll b1 = 2ll*((C[i] * a1) %mod)%mod;
    b1 = (b1 + (sumC *a1) %mod) %mod;
    ll b2 = (4ll*TC)%mod;
    TC = (b1+b2) %mod;
    //cout<<sumC<<"!"<<TT<<"!"<<b1<<"!"<<b2<<"!"<<TC<<endl;
    TT = (2ll*TT)%mod;
    sumC = (sumC +C[i]) %mod;
  }
    cout<<TC<<endl;

    return 0;
}