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 <algorithm>
#include <functional>
#include <iostream>
#include <vector>
using namespace std;
using ll = long long;
constexpr ll MOD = 1e9 + 7;

ll modpow(ll a, ll p, ll m) {
  if (p == 0)
    return 1;
  if (p % 2 == 0) {
    ll d = modpow(a, p / 2, m);
    return d * d % m;
  } else {
    return a * modpow(a, p - 1, m) % m;
  }
}

int main() {
  int n;
  cin >> n;
  vector<ll> c(n + 1);
  for (int i = 1; i <= n; i++) {
    cin >> c[i];
  }
  sort(c.begin() + 1, c.end(), greater<ll>());
  ll ans = 0;
  for (int i = 1; i <= n; i++) {
    ans += c[i] * (i + 1);
    ans %= MOD;
  }
  ans *= modpow(4, n - 1, MOD);
  ans %= MOD;
  cout << ans << endl;
}
