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
import java.util.*;
import java.io.*;

public class Main {
    static long mod = (long) 1e9 + 7;
    public static void main(String[] args) {
        MyScanner sc = new MyScanner();
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
        int n = sc.nextInt();
        Long [] c = new Long[n + 1];
        for (int i = 1; i <= n; i++) c[i] = sc.nextLong();
        Arrays.sort(c, 1, n + 1, Comparator.reverseOrder());
        long ans = 0;
        for (int i = 1; i <= n; i++) {
            long outerPow = pow(2, n - i);
            long firstInner = pow(2, i - 1);
            long secondInner = ((i - 1) * pow(2, i - 2)) % mod;
            long sum = (firstInner + secondInner) % mod;
            long total = (((outerPow * c[i]) % mod) * sum) % mod;
            ans = (ans + total) % mod;
        }
        ans = (ans * pow(2, n)) % mod;
        out.println(ans);
        out.close();
    }


    static long pow(long b, long e) {
        long ans = 1;
        while (e > 0) {
            if (e % 2 == 1)
                ans = ans * b % mod;
            e >>= 1;
            b = b * b % mod;
        }
        return ans;
    }

    static long inv(int x) {
        return pow(x, mod - 2);
    }



    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }


    }

}