Problem: You are given an array of n elements, you must make it a co-prime array in as few moves as possible.

In each move you can insert any positive integral number you want not greater than 109 in any place in the array.

An array is co-prime if any two adjacent numbers of it are co-prime.

In the number theory, two integers a and b are said to be co-prime if the only positive integer that divides both of them is 1.

Input

The first line contains integer n (1 ≤ n ≤ 1000) — the number of elements in the given array.

The second line contains n integers ai (1 ≤ ai ≤ 109) — the elements of the array a.

Output

Print integer k on the first line — the least number of elements needed to add to the array a to make it co-prime.

The second line should contain n + k integers aj — the elements of the array a after adding k elements to it. Note that the new array should be co-prime, so any two adjacent values should be co-prime. Also the new array should be got from the original array a by adding k elements to it.

If there are multiple answers you can print any one of them.

Example

Input

3
2 7 28


Output

1
2 7 9 28

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.StringReader;
import java.io.IOException;
import java.io.Reader;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

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

    static class TaskA {
        private final FastScanner in;
        private final PrintWriter out;

        public TaskA(FastScanner in, PrintWriter out) {
            this.in = in;
            this.out = out;
        }

        public void solve(int testNumber) throws IOException {
            int n = in.nextInt();
            int[] a = in.nextInts(n);
            int ans = 0;
            for (int i = 0; i + 1 < n; i++) {
                int x = a[i];
                int y = a[i + 1];
                if (MathUtils.gcd(x, y) != 1) {
                    ++ans;
                }
            }
            out.println(ans);
            for (int i = 0; i + 1 < n; i++) {
                int x = a[i];
                int y = a[i + 1];
                out.print(x);
                out.print(' ');
                if (MathUtils.gcd(x, y) != 1) {
                    out.print(1);
                    out.print(' ');
                }
            }
            out.print(a[n - 1]);
        }

    }

    static class MathUtils {
        public static long gcd(long p, long q) {
            return q == 0 ? p : gcd(q, p % q);
        }

    }

    static class FastScanner {
        private final BufferedReader br;
        private String line;
        private int pos;

        public FastScanner(String s) throws IOException {
            this(new StringReader(s));
        }

        public FastScanner(InputStream is) throws IOException {
            this(new InputStreamReader(is, "UTF-8"));
        }

        public FastScanner(Reader reader) throws IOException {
            this(new BufferedReader(reader));
        }

        public FastScanner(BufferedReader reader) throws IOException {
            br = reader;
            line = br.readLine();
            pos = 0;
        }

        public String next() throws IOException {
            if (!skipWhitespace()) {
                return null;
            }

            int start = pos;

            while (pos < line.length()) {
                char c = line.charAt(pos);

                if (c == ' ' || c == '\t') {
                    break;
                }

                pos++;
            }

            return line.substring(start, pos);
        }

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

        public int[] nextInts(int n) throws IOException {
            int[] res = new int[n];
            for (int i = 0; i < n; i++) {
                res[i] = nextInt();
            }
            return res;
        }

        private boolean skipWhitespace() throws IOException {
            while (line != null) {
                while (pos < line.length()) {
                    char c = line.charAt(pos);

                    if (c != ' ' && c != '\t') {
                        return true;
                    }

                    pos++;
                }

                line = br.readLine();
                pos = 0;
            }

            return false;
        }

    }
}