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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author prakharjain
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskB solver = new TaskB();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskB {
        int mod = (int) 1e9 + 7;

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.nextInt();

            long[] a = new long[n];

            in.readArray(a, n, 0);

            long[] fac = new long[n + 1];

            fac[0] = 1;

            for (int i = 1; i <= n; i++) {
                fac[i] = i * fac[i - 1];
                fac[i] %= mod;
            }

            long[] inv = new long[n + 1];

            inv[1] = 1;

            for (int i = 2; i <= n; i++) {
                inv[i] = pow(i, mod - 2, mod);
            }

            for (int i = 1; i <= n; i++) {
                inv[i] = inv[i - 1] + inv[i];
                inv[i] %= mod;
            }

            long ans = 0;
            for (int i = 0; i < n; i++) {
                ans += a[i] * inv[n - 1 - i + 1];
                ans %= mod;
                ans += a[i] * inv[i + 1];
                ans %= mod;
                ans -= a[i];

                ans %= mod;
            }

            ans *= fac[n];

            ans %= mod;

            if (ans < 0) {
                ans += mod;
            }

            out.println(ans);

        }

        long pow(long a, long p, int mod) {
            if (p == 0) {
                return 1;
            }

            long t = pow(a, p / 2, mod);

            if (p % 2 != 0) {
                return (((t * t) % mod) * a) % mod;
            } else {
                return (t * t) % mod;
            }
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public void readArray(long[] a, int n, long offset) {
            for (int i = 0; i < n; i++) {
                a[i] = nextLong() - offset;
            }
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void println(long i) {
            writer.println(i);
        }

    }
}

