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>
#define ll long long
#define MOD 1000000007

using namespace std;

ll mypow(int c) {
  ll o = 1, b = 2;
  while(c) {
    if(c & 1)
      o = o * b % MOD;
    c = c / 2;
    b = b * b % MOD;
  }
  return o;
}

int main() {
  ll n, o = 0;
  cin >> n;
  vector<ll> c(n);
  for(int i = 0; i < n; i++)
    cin >> c.at(i);
  sort(c.begin(), c.end());
  for(int i = 0; i < n; i++)
    o = (o + (n + 1 - i) * c.at(i) % MOD) % MOD;
  cout << mypow(2 * n - 2) * o % MOD << endl;
}