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.*;
import java.util.*;
import java.math.*;
 
public class A { 
    
    static boolean ONLINE_JUDGE = false;//change before submit
    static Fast f = new Fast();
    static PrintWriter out = new PrintWriter(System.out); 
    static boolean TEST_CASES = false;
    
    
    static void solve(int TC_NO) {

      int n = ri();

      int[] a = ra(n);
      ArrayList<Integer> l = new ArrayList<>();
      int count = 0;
      l.add(a[0]);
      for(int i = 1 ; i < n; i++){
          if(gcd(a[i],a[i-1])==1) {
          	l.add(a[i]);
          	continue;
          }
          count++;
          l.add(1);
          l.add(a[i]);

      }

      out.println(count);
      for(int i = 0; i < l.size(); i++) out.print(l.get(i)+" ");

      	out.println();
      /*-----WARNING : change [ONLINE_JUDGE = false] before SUBMIT-----*/ 
    }

    static int gcd(int a, int b){
    	
    	while(a!=0 && b!=0){
             if(a>b) a%=b;
             else b%=a;
    	}

    	return a+b;
    }

    
    public static void main(String[] args)throws Exception{

      out = ONLINE_JUDGE? new PrintWriter(new BufferedWriter(new FileWriter("output.txt"))): new PrintWriter(System.out);
      

     
      if(TEST_CASES){
          
          int t = ri();
          int i = 1;
          while(i<=t){
            solve(i);
            i++;
          }

      }

      else {

        solve(1);
      
      }
      
      out.close();

    }

    static int ri() {

      return f.nextInt();
    
    }

    static long rl() {
 
      return f.nextLong();
    
    }

    static double rd() {

       return f.nextDouble();
    
    }

    static char rc() {
      
       return rs().charAt(0);

    }

    static String rs() {

      return f.next();

    }

    static String rS() {
      
       return f.nextLine();
    
    }

    static int[] ra(int n) {
        
      int[] a = new int[n];
      for(int i = 0;i<n;i++) a[i] = ri();
      return a;
        
    }

    static long[] ral(int n) {
        
      long[] a = new long[n];
      for(int i = 0;i<n;i++) a[i] = rl();
      return a;
        
    }

    static double[] rad(int n) {

      double[] a = new double[n];
      for(int i = 0;i<n;i++) a[i] = rd();
      return a;

    }

    static char[] rac() {

        char[] c = rs().toCharArray();

        return c;

    }
    
    static int[][] rm(int n, int m) {
       
       int[][] mat = new int[n][m];

       for(int i = 0; i < n; i++) mat[i] = ra(m);
       
       return mat;

    }

    static char[][] rmc(int n) {
      
      char[][] cmat = new char[n][];
      
      for(int i = 0; i < n; i++) cmat[i] = rac();

      return cmat;

    }

    static void sort(int[] a) {

      ArrayList<Integer> list=new ArrayList<>();
      for (int i:a) list.add(i);
      Collections.sort(list);
      for (int i=0; i<a.length; i++) a[i]=list.get(i);

    }

    static String gcc(int TC_NO) {

         return "Case #"+TC_NO+": ";

    }

    static boolean isLetter(char c){

      return (64<c && c<91) || (96<c && c<123);
    
    }
  
    static class Fast{

       public BufferedReader br;
       public StringTokenizer st;
       
       public Fast(){
            try{
                br = ONLINE_JUDGE? (new BufferedReader(new FileReader("input.txt"))):(new BufferedReader(new InputStreamReader(System.in)));
            }
            catch(Exception e){
              throw new RuntimeException(e);
            }
       }
       
       String next(){
            while(st==null || !st.hasMoreTokens()){
                 try{
                      st=new StringTokenizer(br.readLine());
                 }
                 catch(IOException e){
                      throw new RuntimeException(e);
                 }
                 
            }
                 return st.nextToken();
            }
       int nextInt(){
            return Integer.parseInt(next());
       }
   
       long nextLong(){
            return Long.parseLong(next());
       }
   
       double nextDouble(){
            return Double.parseDouble(next());
       }

       String nextLine() 
          { 
              String str = ""; 
              try
              { 
                  str = br.readLine(); 
              } 
              catch (IOException e) 
              { 
                  e.printStackTrace(); 
              } 
              return str; 
          } 
   
    }

}