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.math.BigInteger;
import java.math.RoundingMode;
import java.text.DecimalFormat;
import java.util.*;
import java.util.Map.Entry;
	
	
	 public class Palindrome {
	
		static double eps=(double)1e-6;
		static long mod=(int)1e9+7;
		public static void main(String args[]){
			InputReader in = new InputReader(System.in);
			OutputStream outputStream = System.out;
			PrintWriter out = new PrintWriter(outputStream);
			Scanner sc=new Scanner(System.in);
			//----------My Code----------
			int n=in.nextInt();
			int a[]=new int[n];
			for(int i=0;i<n;i++){
				a[i]=in.nextInt();
			}
			StringBuilder str=new  StringBuilder();
			str.append(a[0]);
			int total=0;
			for(int i=0;i<n-1;i++){
				if(gcd(a[i],a[i+1])==1)
					str.append(" "+a[i+1]);
				else
				{
					total++;
					str.append(" "+1+" "+a[i+1]);
				}
			}
			System.out.println(total);
			System.out.println(str.toString());
			
			//---------------The End------------------
			out.close();
		}
		
			static class TrieNode{
				boolean isLeaf;
				int b;
				TrieNode[] a=new TrieNode[256];
			}
			
			static void insert(String key,TrieNode root){
				TrieNode temp=root;
				for(int i=0;i<key.length();i++){
				//	System.out.println(i);
					
					if(temp.a[key.charAt(i)]==null){
						temp.a[key.charAt(i)]=new TrieNode();
					}
					temp.a[key.charAt(i)].b+=1;
					temp=temp.a[key.charAt(i)];
					
				}
				temp.isLeaf=true;
			}
			static TrieNode search(String key,TrieNode root){
				TrieNode temp=root;
				for(int i=0;i<key.length();i++){
					
					if(temp.a[key.charAt(i)]==null)
						return null;
					temp=temp.a[key.charAt(i)];
					
				}
				return (temp);
			}
			static String max(String key,TrieNode root){
				TrieNode temp=root;
				String res="";
				for(int i=0;i<key.length();i++){
					
					if(temp.a[(key.charAt(i)-'0')^1]!=null){
					//	System.out.println("Hetr");
					temp=temp.a[(key.charAt(i)-'0')^1];
					res+="1";
					}
					else if(temp.a[(key.charAt(i)-'0')]!=null){
						//System.out.println("Hetr");
						temp=temp.a[(key.charAt(i)-'0')];
						res+="0";
					}
				}
			//	System.out.println(res+"jj");
				return res;
			}
			static void remove(String key,TrieNode root){
				TrieNode temp=root;
				for(int i=0;i<key.length();i++){
					if(temp==null)
						return;
				  if(temp.a[(key.charAt(i)-'0')]!=null&&temp.a[key.charAt(i)-'0'].b>1){
						
						temp.a[(key.charAt(i)-'0')].b--;
						
					
					temp=temp.a[(key.charAt(i)-'0')];
				}
				else
				{
					temp.a[key.charAt(i)-'0']=null;
					return;
				}
				}
				if(temp!=null)
					temp.isLeaf=false;
			}
			
			public static void printSorted(TrieNode node, String s) {
		        for (int ch = 0; ch < node.a.length; ch++) {
		            TrieNode child = node.a[ch];
		            if (child != null){
		                printSorted(child, s + (char)(ch));
		            }
		        }
		        if (node.isLeaf) {
		            System.out.println(s);
		        }
		    }
		private static void permutation(String prefix, String str,HashSet<String> hs) {
		    int n = str.length();
		    if (n == 0) hs.add(prefix);
		    else {
		        for (int i = 0; i < n; i++)
		            permutation(prefix + str.charAt(i), str.substring(0, i) + str.substring(i+1, n),hs);
		    }
		}
		
		
		static int recursiveBinarySearch(int[] sortedArray, int start, int end, int key) {
	
			if (start <= end) {
				int mid = start + (end - start) / 2; 
				if (key < sortedArray[mid]) {
					return recursiveBinarySearch(sortedArray, start, mid-1, key);
	
				} else if (key > sortedArray[mid]) {
					return recursiveBinarySearch(sortedArray, mid+1, end , key);
	
				} else {
					return mid;  
				}
			}
			return -(start + 1); 
		}
	
		static long modulo(long a,long b,long c) {
			long x=1;
			long y=a;
			while(b > 0){
				if(b%2 == 1){
					x=(x*y)%c;
				}
			
				y = (y*y)%c; // squaring the base
				b /= 2;
			}
			return  x%c;
		}
		
		
		static long gcd(long x, long y)
		
		{
			long r=0, a, b;
			a = (x > y) ? x : y; // a is greater number
			b = (x < y) ? x : y; // b is smaller number
			r = b;
			while(a % b != 0)
			{
				r = a % b;
				a = b;
				b = r;
			}
			return r;
		}
		static class pair implements Comparable<pair> {
			int x;
			int y;
			//int i;
			pair(int  xx,int yy){
				
				x=xx;
				y=yy;
				//i=ii;
			}
			@Override
			public int compareTo(pair arg0) {
				return Long.compare(this.y, arg0.y);
			}
		
		}
		static class InputReader {
			public BufferedReader reader;
			public StringTokenizer tokenizer;
	
			public InputReader(InputStream inputstream) {
				reader = new BufferedReader(new InputStreamReader(inputstream));
				tokenizer = null;
			}
	
			public String nextLine(){
				String fullLine=null;
				while (tokenizer == null || !tokenizer.hasMoreTokens()) {
					try {
						fullLine=reader.readLine();
					} catch (IOException e) {
						throw new RuntimeException(e);
					}
					return fullLine;
				}
				return fullLine;
			}
			public String next() {
				while (tokenizer == null || !tokenizer.hasMoreTokens()) {
					try {
						tokenizer = new StringTokenizer(reader.readLine());
					} catch (IOException e) {
						throw new RuntimeException(e);
					}
				}
				return tokenizer.nextToken();
			}
			public long nextLong() {
				return Long.parseLong(next());
			}
			public int nextInt() {
				return Integer.parseInt(next());
			}
		}
	}