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 Int int64_t
 
using namespace std;
 
int main() {
	constexpr Int MOD = 1e9 + 7;
	Int N;
	cin >> N;
	vector<Int> C(N);
	for (int i = 0; i < N; ++i) { cin >> C[i]; }

	vector<Int> x(500010, 0);
	x[0] = 1;
	for (int i = 1; i < x.size(); ++i) {
		x[i] = x[i - 1] * 2 % MOD;
	}

	sort(C.begin(), C.end());
	Int ans = C[N - 1] * x[2 * N - 1] % MOD;
	for (int i = 1; i < N; ++i) {
		Int y = x[N - i - 1] * (N - i + 2) % MOD;
		(ans += C[i - 1] * y % MOD * x[N + i - 1]) %= MOD;
	}
	cout << ans % MOD << endl;

	return 0;
}
