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;
const long long int MOD = 1e9 + 7;

int main(){
    int n;
    cin >> n;

    vector<long long int> c(n);
    for(int i=0; i<n; i++){
        cin >> c[i];
    }
    sort(c.begin(), c.end());
    reverse(c.begin(), c.end());

    long long int ans = 0;
    for(int i=0; i<n; i++){
        ans += c[i] * (i+2);
        ans %= MOD;
    }
    for(int i=0; i<n-1; i++){
        ans *= 4;
        ans %= MOD;
    }
    cout << ans << endl;
    return 0;
}