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
//besmellah
#include <bits/stdc++.h>
using namespace std;

#define int long long

const int maxn = 2e5 + 5, mod = 1e9 + 7;
int P2[maxn], P3[maxn], C[maxn];

int32_t main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	P2[0] = P3[0] = 1;
	for (int i = 1; i < maxn; i++) {
		P2[i] = P2[i - 1] * 2 % mod;
		P3[i] = P3[i - 1] * 4 % mod;
	}
	int n;
	cin >> n;
	for (int i = 0; i < n; i++)
		cin >> C[i];
	sort(C, C + n);
	reverse(C, C + n);
	int ans = 0;
	for (int i = 0; i < n; i++) {
		ans += C[i] * P2[i + 1] % mod * P3[n - i - 1] % mod * (P2[i] + P2[max(0ll, i - 1)] * i % mod) % mod;
		ans %= mod;
//		cout << i << ' ' << C[i] << ' ' << ans << endl;
	}
	cout << ans;
}
