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 <cstdio>
#include <algorithm>
using namespace std;
const long long mod = 1000000007;
int main() {
	int N;
	scanf("%d", &N);
	long long C[N], pow2[N + 1], ans = 0, sbits = 0;
	pow2[0] = 1;
	for (int i = 0; i < N; ++i) scanf("%lld", &C[i]);
	sort(C, C + N);
	for (int i = 1; i <= N; ++i) pow2[i] = pow2[i - 1] * 4 % mod;
	for (int i = 0; i < N; ++i) {
		ans += (sbits * 2 + 2 * pow2[i]) * pow2[N - i - 1] % mod * C[N - i - 1] % mod;
		ans %= mod;
		sbits = (sbits * 4 + pow2[i] * 2) % mod;

	}
	printf("%lld", ans);
	return 0;
}