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;
#define rep(i,n) for(int i = 0; i < (n);i++)
#define sz(x) int(x.size())
typedef long long ll;
typedef pair<int,int> P;
constexpr int mod = 1e9+7;
ll mod_pow(ll x, ll n, ll m = mod){
    if(n == 0)return 1;
    ll res = mod_pow(x*x%m,n/2,m);
    if(n&1) res = res * x % m;
    return res;
}
int main(){
  int n;
  cin >> n;
  vector<ll> c(n);
  rep(i,n) cin >> c[i];
  sort(c.begin(), c.end(), greater<ll>());
  ll d = mod_pow(4, n - 1);
  ll res = 0;
  for (int i = 0; i < n; i++) {
    res += (c[i] * (i + 2)) % mod;
    res %= mod;
  }
  res *= d;
  res %= mod;
  cout << res << endl;
  return 0;
}