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 all(V) V.begin(),V.end()
#define ll long long
#define MOD 1000000007

ll d2[200010];

int main() {
	d2[0] = 1;
	for (int i = 1;i < 200010;i++) d2[i] = d2[i - 1] * 2 % MOD;
	int N;
	cin >> N;
	vector<ll> C(N);
	for (int i = 0;i < N;i++)cin >> C[i];
	sort(all(C));

	ll S, B, D, ans = 0;
	for (int i = 0;i < N;i++) {
		B = N - 1 - i;
		S = i;
		if (B == 0) {
			ans += C[i] * d2[S];
			ans %= MOD;
			continue;
		}
		ans += (C[i] * d2[S] % MOD) * (B * d2[B - 1] % MOD + d2[B]);
		ans %= MOD;
	}
	ans *= d2[N];
	ans %= MOD;
	cout << ans << endl;
}