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 i64 = long long;

int main() {
    constexpr i64 mod = 1000000007;
    int n;
    std::cin >> n;
    std::vector<i64> cost(n), p2(n + 1);
    for (auto &e : cost) std::cin >> e;
    std::sort(cost.begin(), cost.end());
    p2[0] = 1;
    for (int i = 1; i <= n; i++) p2[i] = p2[i - 1] * 2 % mod;

    i64 ret = p2[n - 1] % mod * cost.back() % mod;
    for (int i = 0; i + 1 < n; i++) {
        ret = (ret + p2[i] * (n - i + 1) % mod * p2[n - i - 2] % mod * cost[i] % mod) % mod;
    }

    std::cout << ret * p2[n] % mod << std::endl;

    return 0;
}
