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 rep(i,n) for(int i = 0; i < n; i++)
using namespace std;
typedef long long ll;
typedef pair<int,int> P;
const int MAX_N = 200005;
const ll MOD = 1e9+7;
ll C[MAX_N],pow4[MAX_N];

void calc_pow()
{
	pow4[0] = 1;
	rep(i,MAX_N-1)
	{
		pow4[i+1] = (pow4[i] * 4) % MOD;
	}
}

int main()
{
	calc_pow();
	ll N;
	cin >> N;
	rep(i,N)
	{
		cin >> C[i];
	}
	sort(C,C+N);
	reverse(C,C+N);
	ll ans = 0;
	rep(i,N)
	{
		ans = (ans + (C[i] * pow4[N-1] % MOD) * (i+2) % MOD) % MOD;
	}
	cout << ans << endl;
	return 0;
}