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;

long long const MOD = 1000000007;
long long p[200100];
void init() {
    p[0] = 1;
    for(int i=1; i<200100; ++i) p[i] = p[i - 1] * 2 % MOD;
}

int main() {
    int N; cin >> N;
    vector<long long> C(N);
    for(int i=0; i<N; ++i) cin >> C[i];
    sort(begin(C), end(C));
    
    init();
    long long res = 0;
    for(int i=0; i<N; ++i) {
        long long tmp = p[N - 1];
        if(N > 1) tmp = (tmp + (N - 1 - i) * p[N - 2] % MOD) % MOD;
        tmp = tmp * C[i] % MOD;
        res = (res + tmp) % MOD;
    }
    res = res * p[N] % MOD;
    cout << res << endl;
}