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:
/*
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 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */

import java.io.File;
import java.io.FileNotFoundException;
import java.util.*;

/**
 *
 * @author Julian Leonardo Paez Silva
 */
public class CoPrimeArray {

    /**
     * @param args the command line arguments
     * @throws java.io.FileNotFoundException
     */
    public static void main(String[] args) throws FileNotFoundException {
        In in = new In();

        int n = in.nextInt();
        int[] a = in.nextInts();

        List<Integer> lista = new ArrayList(n * 2);
        lista.add(a[0]);
        int k = 0;
        for (int i = 0; i < a.length - 1; i++) {
            int a1 = a[i], a2 = a[i + 1];
            int mcd = mcd(a1, a2);
            if (mcd != 1) {
                k++;
                lista.add(1);
            }
            lista.add(a2);
        }

        System.out.println(k);
        lista.stream().forEach((l) -> {
            System.out.print(l + " ");
        });
    }

    private static int mcd(int a, int b) {
        while (a % b != 0) {
            int c = b;
            b = a % b;
            a = c;
        }

        return b;
    }

    private static class In {

        private final Scanner scan;

        public In() throws FileNotFoundException {
            File f = new File("CoPrimeArray.in");
            if (f.exists()) {
                this.scan = new Scanner(f);
            } else {
                this.scan = new Scanner(System.in);
            }
        }

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

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

        public String nextString() {
            return scan.nextLine();
        }

        public int[] nextInts() {
            String[] line = scan.nextLine().split(" ");
            int[] ints = new int[line.length];

            for (int i = 0; i < ints.length; i++) {
                ints[i] = Integer.parseInt(line[i]);
            }
            return ints;
        }

        public long[] nextLongs() {
            String[] line = scan.nextLine().split(" ");
            long[] longs = new long[line.length];

            for (int i = 0; i < longs.length; i++) {
                longs[i] = Long.parseLong(line[i]);
            }
            return longs;
        }

        public String[] nextStrings() {
            return scan.nextLine().split(" ");
        }

        public double[] nextDoubles() {
            String[] line = scan.nextLine().split(" ");
            double[] doubles = new double[line.length];

            for (int i = 0; i < doubles.length; i++) {
                doubles[i] = Double.parseDouble(line[i]);
            }
            return doubles;
        }

    }

}