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 rep(i, n) for(int (i) = 0; i < (n); ++(i))

typedef long long ll;
const ll MOD = 1e9 + 7;

ll modpow(ll a, ll n) {
  ll ret = 1LL;
  while(n > 0) {
    if(n & 1) ret = a * ret % MOD;
    a = a * a % MOD;
    n >>= 1;
  }

  return ret;
}

int main() {
  int N;
  std::cin >> N;

  std::vector<ll> C(N);
  rep(i, N) {
    std::cin >> C[i];
  }
  std::sort(C.rbegin(), C.rend());

  ll ans = 0;

  rep(i, N) {
    ans += C[i] * (i + 2) % MOD;
    ans %= MOD;
  }
  ans *= modpow(2, 2 * (N - 1));
  ans %= MOD;

  std::cout << ans << '\n';
}
