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.*;

class Main{
    public static void main(String[] args) {
        FastScanner fs = new FastScanner();
        int n = fs.nextInt();
        int[] c = new int[n];
        for (int i = 0; i < n; i++) {
            c[i] = -fs.nextInt();
        }
        Arrays.sort(c);
        long modSum = 0;
        
        int mod = 1000000007;

        long pow = n > 1 ?MOD.getPowMod(2,n-2,mod) : 1L;
        if(n==1){
            modSum +=-c[0];
            modSum %=mod;
        }else{
            for(int i=0;i<n;i++){
                modSum +=pow*(i+2)%mod*(-c[i])%mod;
                modSum %=mod;
            }
        }

        long npow2 = MOD.getPowMod(2,n,mod);
        System.out.println(npow2*modSum%mod);

    }

    static class FastScanner {
        private final InputStream in = System.in;
        private final byte[] buffer = new byte[1024];
        private int ptr = 0;
        private int buflen = 0;

        private boolean hasNextByte() {
            if (ptr < buflen) {
                return true;
            } else {
                ptr = 0;
                try {
                    buflen = in.read(buffer);
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (buflen <= 0) {
                    return false;
                }
            }
            return true;
        }

        private int readByte() {
            if (hasNextByte()) return buffer[ptr++];
            else return -1;
        }

        private boolean isPrintableChar(int c) {
            return 33 <= c && c <= 126;
        }

        public boolean hasNext() {
            while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
            return hasNextByte();
        }

        public String next() {
            if (!hasNext()) throw new NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while (isPrintableChar(b)) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }

        public long nextLong() {
            if (!hasNext()) throw new NoSuchElementException();
            long n = 0;
            boolean minus = false;
            int b = readByte();
            if (b == '-') {
                minus = true;
                b = readByte();
            }
            if (b < '0' || '9' < b) {
                throw new NumberFormatException();
            }
            while (true) {
                if ('0' <= b && b <= '9') {
                    n *= 10;
                    n += b - '0';
                } else if (b == -1 || !isPrintableChar(b)) {
                    return minus ? -n : n;
                } else {
                    throw new NumberFormatException();
                }
                b = readByte();
            }
        }

        public int nextInt() {
            long nl = nextLong();
            if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
            return (int) nl;
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }
    }
}
class MOD {
    static long[] fac,inv,finv;
    static int mod = 1000000007;

    public static long getPowMod(long a, long x,long mod){
        long res = 1;
        while(x > 0){
            if((x&1)==1){
                res = (res*a)%mod;
            }
            x>>=1;
            a = (a*a)%mod;
        }
        return res;
    }
    public static long getFactorialMod(long n,long mod){
        if(n==0){
            return 1;
        }else{
            return (n*getFactorialMod(n-1, mod))%mod;
        }
    }

    public static long nCkMod(long n,long k,long mod){
        if(n < k){
            return 0;
        }else{
            long nMod = getFactorialMod(n, mod);
            long kinvMod = getPowMod(getFactorialMod(k, mod), mod-2, mod);
            long n_kinvMod = getPowMod(getFactorialMod(n-k, mod), mod-2, mod);
            long x = (nMod*kinvMod)%mod;
            return (x*n_kinvMod)%mod;
        }
    }

    public static void COMinit(int max){
        fac = new long[max];
        inv = new long[max];
        finv = new long[max];
        fac[0] = fac[1] = 1;
        finv[0] = finv[1] = 1;
        inv[1] = 1;
        for(int i=2;i<max;i++){
            fac[i] = fac[i-1]*i%mod;
            inv[i] = mod-inv[mod%i]*(mod/i)%mod;
            finv[i] = finv[i-1]*inv[i]%mod;
        }
    }
    public static long nCkMod2(int n,int k){
        if(n < k)return 0;
        return fac[n]*(finv[k]*finv[n-k]%mod)%mod;
    }
}