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 <iostream>
#include <vector>
#include <algorithm>
using namespace std;

//  a^b % m
long long powmod(long long a, long long b, long long m)
{
    long long r = 1;
    for (; b>0; b>>=1, a=a*a%m)
        if (b&1)
            r = r*a%m;
    return r;
}

int main()
{
    int N;
    cin>>N;
    vector<long long> C(N);
    for (long long &c: C)
        cin>>c;

    sort(C.begin(), C.end());
    long long M = 1000000007;
    long long ans = 0;
    for (int i=N-1; i>=0; i--)
    {
        ans += C[i]*powmod(2, N-2+(M-1), M)%M*(2+N-i-1)%M;
        ans %= M;
    }
    ans *= powmod(2, N, M);
    ans %= M;
    cout<<ans<<endl;
}
