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;

const int MOD = 1000000007;

ll pow(int n){
  ll p = 1;
  for (int i = 0; i < n; i++) {
    p = p * 4 % MOD;
  }
  return p;
}

int main() {
  
  int N;
  cin >> N;
  int POW = pow(N-1);
  
  vector<ll> c;
  for (int i = 0; i < N; i++) {
    ll n;
    cin >> n;
    c.push_back(n);
  }
  sort(c.begin(), c.end());
  
  
  
  
  ll ans = 0;
  for (int i = 0; i < N; i++) {
    ll p = 1;
    p = (p * (N-i+1)) % MOD;
    p = (p * c[i]) % MOD;
    ans = (ans + p) % MOD;
  }
  ans = (ans * POW) % MOD; 
  
  cout << ans << endl;
}
