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;
const int Mod = 1e9+7;
int N;
vector<int> C;


ll powmod(ll a, ll b, ll m) {
    ll c = 1;
    for (; b; b >>= 1, a = (ll)a * a % m) {
        if (b & 1) c = c * a % m;
    }
    return c;
}


void solve()
{
    sort(C.begin(), C.end());    
    ll d = (N == 1) ? 0 : powmod(2, N - 2, Mod);
    ll w = (N == 1) ? 1 : (N + 1) * d % Mod;
    ll ans = 0;
    for (int i = 0; i < N; i++) {
        ans = (ans + C[i] * w) % Mod;
        w = (w - d + Mod) % Mod;
    }
    ans = ans * powmod(2, N, Mod) % Mod;
    cout << ans << endl;
}


int main()
{
    cin >> N;
    C.resize(N);
    for (int i = 0; i < N; i++) cin >> C[i];
    solve();
    return 0;
}
