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;
typedef long long int64;
const int64 MOD = 1000000007;

template<class T>
T mod_pow(T x, T n, const T mod) {
    T res = 1;
    while(n > 0) {
        if(n & 1) res = res * x % mod;
        x = x * x % mod;
        n = n >> 1;
    }
    return res;
}

int main() {
    int N; cin >> N;
    vector<int64> C(N);
    for(int i = 0; i < N; ++i) cin >> C[i];
    sort(C.begin(), C.end(), greater<int64>());
    int64 ans = 0, A = mod_pow(4LL, (int64)N - 1, MOD);
    for(int i = 1; i <= N; ++i) {
        ans += A * C[i - 1] % MOD * (i + 1);
        ans %= MOD;
    }
    cout << ans << '\n';
    return 0;
}
