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 (long long i = 0; i < (n); ++i)
using namespace std;
using ll = long long;
using P = pair<ll,ll>;
const ll MOD = 1000000007;
const ll INF = 10000000000000;
#define all(v) v.begin(), v.end()

ll modPow(ll a, ll n) {
  if (n == 0) return 1; // 0乗にも対応する場合
  if (n == 1) return a % MOD;
  if (n % 2 == 1) return (a * modPow(a, n - 1)) % MOD;
  ll t = modPow(a, n / 2);
  return (t * t) % MOD;
}

int main(){
  ll N,m=0;
  cin >> N;
  vector<ll> C(N);
  rep(i,N){
    cin >> C.at(i);
  }
  sort(all(C));
  reverse(all(C));
  rep(i,N){
    m+=(i+2)*C.at(i);
    m%=MOD;
  }
  m*=modPow(4,N-1);
  m%=MOD;
  cout << m << endl;   
  
}
