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.BufferedReader;
import java.io.EOFException;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.io.UncheckedIOException;
import java.lang.reflect.Array;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Deque;
import java.util.List;
import java.util.Objects;
import java.util.regex.Pattern;
import java.util.stream.Collectors;

public class Main {
    public void exec() {
        int n = stdin.nextInt();
        int[] a = stdin.nextIntArray(n);

        List<Integer> d = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            d.add(a[i]);
            if (i < n-1 && gcd(a[i], a[i+1]) != 1) {
                d.add(1);
            }
        }

        String line = d.stream().map(Objects::toString).collect(Collectors.joining(" "));
        stdout.println(d.size()-n);
        stdout.println(line);
    }

    public int gcd(int x, int y) {
        if (x < y) {
            int tmp = x;
            x = y;
            y= tmp;
        }

        while (y > 0) {
            int mod = x % y;
            x = y;
            y = mod;
        }

        return x;
    }

    public String join(int[] a, String delimiter) {
        return Arrays.stream(a).mapToObj(String::valueOf).collect(Collectors.joining(delimiter));
    }


    private static final Stdin stdin = new Stdin();
    private static final Stdout stdout = new Stdout();

    public static void main(String[] args) {
        try {
            new Main().exec();
        } finally {
            stdout.flush();
        }
    }

    public static class Stdin {
        private BufferedReader stdin;
        private Deque<String> tokens;
        private Pattern delim;

        public Stdin() {
            stdin = new BufferedReader(new InputStreamReader(System.in));
            tokens = new ArrayDeque<>();
            delim = Pattern.compile(" ");
        }

        public String nextString() {
            try {
                if (tokens.isEmpty()) {
                    String line = stdin.readLine();
                    if (line == null) {
                        throw new UncheckedIOException(new EOFException());
                    }
                    delim.splitAsStream(line).forEach(tokens::addLast);
                }
                return tokens.pollFirst();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

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

        public double nextDouble() {
            return Double.parseDouble(nextString());
        }

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

        public String[] nextStringArray(int n) {
            String[] a = new String[n];
            for (int i = 0; i < n; i++) a[i] = nextString();
            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 double[] nextDoubleArray(int n) {
            double[] a = new double[n];
            for (int i = 0; i < n; i++) a[i] = nextDouble();
            return a;
        }

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

    public static class Stdout {
        private PrintWriter stdout;

        public Stdout() {
            stdout =  new PrintWriter(System.out, false);
        }

        public void printf(String format, Object ... args) {
            String line = String.format(format, args);
            if (line.endsWith(System.lineSeparator())) {
                stdout.print(line);
            } else {
                stdout.println(line);
            }
        }

        public void println(Object ... objs) {
            String line = Arrays.stream(objs).map(Objects::toString).collect(Collectors.joining(" "));
            stdout.println(line);
        }

        public void printDebug(Object ... objs) {
            String line = Arrays.stream(objs).map(this::deepToString).collect(Collectors.joining(" "));
            stdout.printf("DEBUG: %s%n", line);
            stdout.flush();
        }

        private String deepToString(Object o) {
            if (o == null) {
                return "null";
            }

            // 配列の場合
            if (o.getClass().isArray()) {
                int len = Array.getLength(o);
                String[] tokens = new String[len];
                for (int i = 0; i < len; i++) {
                    tokens[i] = deepToString(Array.get(o, i));
                }
                return "{" + String.join(",", tokens) + "}";
            }

            return Objects.toString(o);
        }

        private void flush() {
            stdout.flush();
        }
    }
}