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, a) for(int i=0; i<(int)(a); i++)
typedef long long ll;
const ll mod = 1000000007;

const int MAX = 510000;
ll fac[MAX], finv[MAX], inv[MAX];

ll modpow(ll a, ll n)
{
  ll res=1;
  while (n>0) {
    if (n&1) res = res*a % mod;
    a = a*a % mod;
    n >>= 1;
  }
  return res;
}

int main()
{
  ll n; cin >> n;
  vector<ll> c(n);
  rep(i, n) cin >> c[i];
  sort(c.rbegin(),c.rend());

  ll ans = 0;
  rep(i, n) {
    ll tmp = c[i] * (i+2) % mod;
    ans = (ans + tmp) % mod;
  }
  ans = (ans * modpow(4, n-1)) % mod;
  cout << ans << endl;

  return 0;
}
