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 int long long
const int MOD = 1000000007;

signed main() {
	cin.tie(0);
	ios::sync_with_stdio(false);
	int N;
	cin >> N;
	vector<int> p2(N + 5);
	p2[0] = 1;
	for (int i = 1; i < p2.size(); i++) {
		p2[i] = (p2[i - 1] * 2) % MOD;
	}
	vector<int> A(N);
	int res = 0;
	for (int i = 0; i < N; i++) {
		cin >> A[i];
	}
	sort(A.begin(), A.end());
	for (int i = 0; i < N; i++) {
		int coef = p2[N - i];
		coef = (coef + p2[N - i - 1] * (N - i - 1)) % MOD;
		coef = (coef * p2[i]) % MOD;
		res = (res + A[i] * coef) % MOD;
	}
	res = (res * p2[N - 1]) % MOD;
	cout << res << endl;
}