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 {
    public static void main(String[] args) throws Exception {
        FastScanner sc = new FastScanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        long mod = (long)1e9+7;
        int n = sc.nextInt();
        Long[] c = new Long[n];
        for(int i = 0; i < n; i++){
            c[i] = sc.nextLong();
        }
        Arrays.sort(c,Comparator.reverseOrder());
        long ans = 0;
        if(n == 1){
            pw.println(c[0]*2%mod);
        }else{
            long n2 = rep2(2,n-2,mod);
            long n1 = rep2(2,n-1,mod);
            for(int i = 0; i < n; i++){
                long fac = (n2 * i)%mod+n1;
                ans += fac%mod * c[i]%mod;
                ans %= mod;
            }
            pw.println(ans*rep2(2,n,mod)%mod);
        }
        pw.flush();
    }

    static class GeekInteger {
        public static void save_sort(int[] array) {
            shuffle(array);
            Arrays.sort(array);
        }
 
        public static int[] shuffle(int[] array) {
            int n = array.length;
            Random random = new Random();
            for (int i = 0, j; i < n; i++) {
                j = i + random.nextInt(n - i);
                int randomElement = array[j];
                array[j] = array[i];
                array[i] = randomElement;
            }
            return array;
        }
 
    }
    
    private static long rep2(long b, long n, long mod){
        if(n == 0) return 1;
        long bn = rep2(b,n/2,mod);
        if(n % 2 == 0){
            return (bn*bn)%mod;
        }else{
            return (bn*bn)%mod*b%mod;
        }
    }
}

class Combination {
    final static long mod = (long)Math.pow(10,9)+ 7;
    private static long[] fact, ifact;
    public Combination(int n){
        fact = new long[n+1];
        ifact = new long[n+1];
        fact[0] = 1;
        long ln = n;
        for (long i = 1; i <= ln; ++i){
            int ii = (int)i;
            fact[ii] = fact[ii-1]%mod * i % mod;
        }
        ifact[n] = pow(fact[n],this.mod-2);
        for (int i = n; i >= 1; --i){
            int ii = (int)i;
            ifact[ii-1] = ifact[ii]%mod*i%mod;
        }
    }
    
    public static long comb(int n, int k){
        if (k < 0 || k > n) return 0;
        return fact[n] % mod * ifact[k] % mod * ifact[n-k] % mod;
    }
    
    public static long perm(int n, int k){
        return comb(n,k) * fact[k] % mod;
    }
    
    public static long pow(long a,long b) {
        long ret = 1;
        long tmp = a;
        while(b>0) {
            if((b&1)==1){
                ret = (ret * tmp) % mod;
            }
            tmp = (tmp * tmp) % mod;
            b = b>>1;
        }
        return ret;
    }
}


class FastScanner {
    private BufferedReader reader = null;
    private StringTokenizer tokenizer = null;
    public FastScanner(InputStream in) {
        reader = new BufferedReader(new InputStreamReader(in));
        tokenizer = null;
    }

    public String next() {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    public String nextLine() {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                return reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken("\n");
    }

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

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

    public double nextDouble() {
         return Double.parseDouble(next());
    }
    
    public String[] nextArray(int n) {
        String[] a = new String[n];
        for (int i = 0; i < n; i++)
            a[i] = next();
        return a;
    }

    public int[] nextIntArray(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = nextInt();
        return a;
    }

    public long[] nextLongArray(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++)
            a[i] = nextLong();
        return a;
    } 
}
