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 ll long long
#define pb push_back
#define mp make_pair
using namespace std;
const int maxn = 200100;
const ll mod = 1e9 + 7;
ll arr[maxn], n;

int main() {
	cin>>n;
	ll pow4 = 1LL;
	for(int i=1;i<=n;i++) {
		cin>>arr[i];
		if(i < n) {
			pow4 *= 4LL;
			pow4 %= mod;
		}
	}

	sort(arr+1, arr+n+1);
	reverse(arr+1, arr+n+1);

	ll sum = 0LL;
	for(int i=1;i<=n;i++) {
		sum += ((1LL * arr[i] * (i+1))%mod);
		sum %= mod;
	}

	ll result = pow4 * sum;
	cout<<result % mod;
}