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;
using ll = long long;
const ll MOD = 1e9 + 7;
const int N = 2e5 + 5;

int n, c[N];
int main() {
  ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
  cin >> n;
  for (int i = 1; i <= n; ++i) cin >> c[i];
  sort(c + 1, c + 1 + n, greater<int>());

  ll res = 0;
  for (int i = 1; i <= n; ++i) {
    (res += 1LL * c[i] * (i + 1)) %= MOD;
  }
  for (int i = 1; i < n; ++i) {
    (res *= 4LL) %= MOD;
  }
  cout << res;
  return 0;
}