There are N blocks arranged in a row, numbered 1 to N from left to right. Each block has a weight, and the weight of Block i is A_i. Snuke will perform the following operation on these blocks N times:

* Choose one block that is still not removed, and remove it. The cost of this operation is the sum of the weights of the blocks that are connected to the block being removed (including itself). Here, two blocks x and y ( x \leq y ) are connected when, for all z ( x \leq z \leq y ), Block z is still not removed.



There are N! possible orders in which Snuke removes the blocks. For all of those N! orders, find the total cost of the N operations, and calculate the sum of those N! total costs. As the answer can be extremely large, compute the sum modulo 10^9+7.

Constraints

* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
A_1 A_2 ... A_N


Output

For all of the N! orders, find the total cost of the N operations, and print the sum of those N! total costs, modulo 10^9+7.

Examples

Input

2
1 2


Output

9


Input

4
1 1 1 1


Output

212


Input

10
1 2 4 8 16 32 64 128 256 512


Output

880971923
import java.io.*;
import java.util.*;
import java.math.*;
// import java.awt.Point;
 
public class Main {
    InputStream is;
    PrintWriter out;
    String INPUT = "";
 
    static int mod = 1_000_000_007;
    long inf = Long.MAX_VALUE;

    void solve(){
        int n = ni();
        long[] a = new long[n];
        for(int i = 0; i < n; i++){
            a[i] = nl();
        }
        long[] l1 = new long[n+1];
        long[] l2 = new long[n+1];

        long[] cum1 = new long[n+1];
        long[] cum2 = new long[n+1];

        int mod = 1000000007;
        int[][] fif = enumFIF(1000000, mod);

        for(int i = 0; i <= n-1; i++){
            l1[i] = C(n,i+1,mod,fif)%mod * fif[0][i]%mod * fif[0][n-i-1]%mod;
            cum1[i+1] += cum1[i] + l1[i];
            cum1[i+1] %= mod;
        }

        for(int i = 0; i <= n-2; i++){
            l2[i] = C(n,i+2,mod,fif)%mod * 2 * fif[0][i]%mod * fif[0][n-i-2]%mod;
            cum2[i+1] += cum2[i] + l2[i];
            cum2[i+1] %= mod;
        }

        // for(int i = 0; i < n; i++){
        //     out.println(l1[i]);
        //     out.println(l2[i]);
        // }
        long sum = 0;
        long[] res1 = new long[n];
        long[] res2 = new long[n];
        for(int i = 1; i <= n/2; i++){
            res2[i] += res2[i-1] + cum2[n-i] - cum2[i];
            res2[i] = (res2[i]+10000000l*mod)%mod;
        }

        for(int i = 0; i <= n/2; i++){
            if(i==0){
                res1[i] = cum1[n];
            }
            else{
                res1[i] = res1[i-1];
                res1[i] -= l1[i];
                res1[i] += l1[n-i];
            }
            res1[i] = (res1[i]+10000000l*mod)%mod;
        }
        for(int i = 0; i < n; i++){
            long t1 = (i<=n/2 ?  res1[i] : res1[n-i-1]);
            long t2 = (i<=n/2 ?  res2[i] : res2[n-i-1]);
            sum += a[i] * t2 % mod;
            sum %= mod;
            sum += a[i] * t1 % mod;
            sum %= mod;
            // out.println(t1);
            // out.println(t2);
        }
        // for(int i = 0; i < n; i++){
        //     sum += a[i]*fif[0][n];
        //     sum %= mod;
        // }

        out.println(sum%mod);
    }

    public static long C(int n, int r, int mod, int[][] fif) {
        if (n < 0 || r < 0 || r > n)
            return 0;
        return (long) fif[0][n] * fif[1][r] % mod * fif[1][n - r] % mod;
    }

    
    public static int[][] enumFIF(int n, int mod) {
        int[] f = new int[n + 1];
        int[] invf = new int[n + 1];
        f[0] = 1;
        for (int i = 1; i <= n; i++) {
            f[i] = (int) ((long) f[i - 1] * i % mod);
        }
        long a = f[n];
        long b = mod;
        long p = 1, q = 0;
        while (b > 0) {
            long c = a / b;
            long d;
            d = a;
            a = b;
            b = d % b;
            d = p;
            p = q;
            q = d - c * q;
        }
        invf[n] = (int) (p < 0 ? p + mod : p);
        for (int i = n - 1; i >= 0; i--) {
            invf[i] = (int) ((long) invf[i + 1] * (i + 1) % mod);
        }
        return new int[][] { f, invf };
    }

    void run() throws Exception
    {
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);
        long s = System.currentTimeMillis();
        solve();
        out.flush();
        if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
    }
    
    public static void main(String[] args) throws Exception { new Main().run(); }
    
    private byte[] inbuf = new byte[1024];
    private int lenbuf = 0, ptrbuf = 0;
    
    private int readByte()
    {
        if(lenbuf == -1)throw new InputMismatchException();
        if(ptrbuf >= lenbuf){
            ptrbuf = 0;
            try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
            if(lenbuf <= 0)return -1;
        }
        return inbuf[ptrbuf++];
    }
    
    private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
    private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
    
    private double nd() { return Double.parseDouble(ns()); }
    private char nc() { return (char)skip(); }
    
    private String ns()
    {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while(!(isSpaceChar(b) && b != ' ')){
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    
    private char[] ns(int n)
    {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while(p < n && !(isSpaceChar(b))){
            buf[p++] = (char)b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }
    
    private char[][] nm(int n, int m)
    {
        char[][] map = new char[n][];
        for(int i = 0;i < n;i++)map[i] = ns(m);
        return map;
    }
    
    private int[] na(int n)
    {
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = ni();
        return a;
    }
    
    private int ni()
    {
        int num = 0, b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private long nl()
    {
        long num = 0;
        int b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); }
 
}
