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 <iostream>
#include <vector>
#define MOD 1000000007
using namespace std;
typedef long long ll;
ll mod_pow(ll x, ll n, ll mod) {
  ll res = 1;
  while (n > 0) {
    if (n & 1) {
      res = res * x % mod;
    }
    x = x * x % mod;
    n /= 2LL;
  }
  return res;
}

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