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;
using ll = long long;

#define mod 1000000007
#define MAX_N 400005
ll pow2[MAX_N];
void pow2_init(){
    pow2[0] = 1;
    for (int i = 1; i < MAX_N; ++i) {
        pow2[i] = pow2[i-1] * 2 % mod;
    }
}

int main() {
    pow2_init();
    int N;
    cin >> N;
    vector<ll>C(N);
    for (int i = 0; i < N; ++i) {
        cin >> C[i];
    }
    sort(C.begin(), C.end());
    ll ans = 0;
    for (int i = 0; i < N; ++i) {
        ll temp = N - i + 1;
        temp *= pow2[N-1] * pow2[N-1] % mod;
        temp %= mod;
        temp = temp * C[i] % mod;
        ans += temp;
        ans %= mod;
    }
    cout << ans << "\n";
    return 0;
}