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 ll long long

int N;
ll C[202020];
ll mo=1000000007;

void solve() {
    int i, j, k, l, r, x, y;
    string s;
    cin >> N;
    for (int i = 0; i < N; ++i) cin >> C[i];
    sort(C, C + N);
    reverse(C, C + N);
    ll p = 1, q = 1;
    for (int i = 0; i < N; ++i) {
        q = q * 2 % mo;
    }
    ll sum = 1, ret = 0;
    for (int i = 0; i < N; ++i) {
        q = q * (mo + 1) / 2 % mo;
		(ret+=(C[i]*sum)%mo*q)%=mo;
		sum=(sum*2+p)%mo;
		p=p*2%mo;
    }
    cout<<ret*p%mo<<endl;
}


int main() {
    solve();
}