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:
					/*
					 * Author- Priyam Vora
					 * BTech 2nd Year DAIICT
					 */
					
					        import java.io.*;
					     
					        import java.math.BigInteger;
					        import java.util.*;
					import java.util.Map.Entry;
					
					import javax.print.attribute.SetOfIntegerSyntax;
					     
					        public class Graph1 {
					        	
					    	    private static InputStream stream;
					        	private static byte[] buf=new byte[1024];
					        	private static int curChar;
					        	private static int numChars;
					        	private static SpaceCharFilter filter;
					        	private static PrintWriter pw;
					        	private static long count=0;
					            public static void main(String args[] ) throws Exception 
					            {
					            	InputReader(System.in);
					        		pw=new PrintWriter(System.out);
					        		//ans();
					        		soln();
					        		pw.close();
					            }
					     
					            public static long gcd(long x,long y)
					            {
					            	if(x%y==0)
					            		return y;
					            	else
					            		return gcd(y,x%y);
					            }
					            public static int gcd(int x,int y)
					            {
					            	if(x%y==0)
					            		return y;
					            	else 
					            		return gcd(y,x%y);
					            }
					            
					
					
					public static long pow(long n,long p,long m)
					{
						 long  result = 1;
						  if(p==0)
						    return 1;
						if (p==1)
						    return n;
						while(p!=0)
						{
						    if(p%2==1)
						        result *= n;
						    if(result>=m)
						    result%=m;
						    p >>=1;
						    n*=n;
						    if(n>=m)
						    n%=m;
						}
						return result;
					}
					public static long pow(long n,long p)
					{
						long  result = 1;
						  if(p==0)
						    return 1;
						if (p==1)
						    return n;
						while(p!=0)
						{
						    if(p%2==1)
						        result *= n;	    
						    p >>=1;
						    n*=n;	    
						}
						return result;
					
					}
					public static long printSubsets(int set[],int pow,long sum)
						{
						long ans=0;
							int n = set.length;
					
							// Run a loop for printing all 2^n
							// subsets one by obe
							for (int i = 0; i < (1<<n); i++)
							{
								int a[]=new int[n];
								
								int count=0;
					
								// Print current subset
								for (int j = 0; j < n; j++)
					
									// (1<<j) is a number with jth bit 1
									// so when we 'and' them with the
									// subset number we get which numbers
									// are present in the subset and which
									// are not
									if ((i & (1 << j)) > 0)
										{
										
										a[count]=set[j];
										count++;
										//System.out.print(set[j] + " ");
										}
					long tot=0;
							for(int t=0;t<count;t++){
							tot+=a[t];	
								//pw.print(a[t]+" ");
							}
						//	System.out.println(tot+" "+sum);
							if((tot)>=pow && (sum-tot)>=pow){
							ans++;
							}
							}//System.out.println(sum+"-sum "+l+" -l");
							return ans;
							}
					
						 
						// remove N elements in equal steps starting at specific point
						static List<Integer> josephus(int N, int step, int start)
						{
						    if (N < 1 || step < 1 || start < 1) return null;
					
						    List<Integer> p = new LinkedList<Integer>();
						    for (int i = 0; i < N; i++)
						        p.add(i+1);
					
						    List<Integer> r = new LinkedList<Integer>();
						    int i = (start - 2) % N;
						    for (int j = N; j > 0; j--) {
						        i = (i + step) % N--;
						        r.add(p.remove(i--));
						    }
					
						    return r;
						}
					
						 
						 
						 public static long fact(long n){
							 if(n==0)
								 return 1;
							 else
								 return (long)n*(long)fact(n-1);
							 
						 }
					
					
					public static int[] radixSort(int[] f)
					{
						int[] to = new int[f.length];
						{
							int[] b = new int[65537];
							for(int i = 0;i < f.length;i++)b[1+(f[i]&0xffff)]++;
							for(int i = 1;i <= 65536;i++)b[i]+=b[i-1];
							for(int i = 0;i < f.length;i++)to[b[f[i]&0xffff]++] = f[i];
							int[] d = f; f = to;to = d;
						}
						{
							int[] b = new int[65537];
							for(int i = 0;i < f.length;i++)b[1+(f[i]>>>16)]++;
							for(int i = 1;i <= 65536;i++)b[i]+=b[i-1];
							for(int i = 0;i < f.length;i++)to[b[f[i]>>>16]++] = f[i];
							int[] d = f; f = to;to = d;
						}
						return f;
					} 
					
					public static int nextPowerOf2(final int a)
					{
					    int b = 1;
					    while (b < a)
					    {
					        b = b << 1;
					    }
					    return b;
					}
					     
					        
					    public static boolean PointInTriangle(int p1, int p2, int p3, int p4, int p5, int p6, int p7, int p8)
					    {
					    int s = p2 * p5 - p1 * p6 + (p6 - p2) * p7 + (p1 - p5) * p8;
					    int t = p1 * p4 - p2 * p3 + (p2 - p4) * p7 + (p3 - p1) * p8;
					     
					    if ((s < 0) != (t < 0))
					    return false;
					     
					    int A = -p4 * p5 + p2 * (p5 - p3) + p1 * (p4 - p6) + p3 * p6;
					    if (A < 0.0)
					    {
					    s = -s;
					    t = -t;
					    A = -A;
					    }
					    return s > 0 && t > 0 && (s + t) <= A;
					    }
					     
					      public static float area(int x1, int y1, int x2, int y2, int x3, int y3){
					    	  return (float)Math.abs((x1*(y2-y3) + x2*(y3-y1)+ x3*(y1-y2))/2.0);
					      }
					      public static boolean isPrime(int n)
					      {
					          // Corner cases
					          if (n <= 1)  return false;
					          if (n <= 3)  return true;
					       
					          // This is checked so that we can skip 
					          // middle five numbers in below loop
					          if (n%2 == 0 || n%3 == 0) return false;
					       
					          for (int i=5; i*i<=n; i=i+6)
					              if (n%i == 0 || n%(i+2) == 0)
					                 return false;
					       
					          return true;
					      }
					     
					     
					    //merge Sort
					            
					            public static void Merge_sort(int a[]){
					            	int len=a.length;
					            	if(len <2)
					            		return ;
					            	int mid=len/2;
					            	int l[]=new int[mid];
					            	int r[] =new int[len-mid];
					            	for(int i=0;i<mid;i++)
					            		l[i]=a[i];
					            	for(int i=mid;i<len;i++)
					            		r[i-mid]=a[i];
					            	
					            	Merge_sort(l);
					            	Merge_sort(r);
					            	Merge(l,r,a);
					            }
					            	
					            public static void Merge(int []l,int[]r,int a[]){
					            	int nl=l.length;
					            	int nr=r.length;
					            	int i=0,j=0,k=0;
					            	
					            	while(i <nl && j<nr){
					            		if(l[i] > r[j]){
					            			a[k]=l[i];
					            			k++;
					            			i++;
					            		}
					            		else{
					            			a[k]=r[j];
					            			k++;
					            			j++;
					            		}
					            		
					            		while(i<nl){
					            			a[k]=l[i];
					            			k++;
					            			i++;
					            		}
					            		while(j<nr){
					            			a[k]=r[j];
					            			k++;
					            			j++;
					            		}
					            	}
					            }
					      
					        	
					        public static boolean isSubSequence(String large,String small,int largeLen,int smallLen){
					        //base cases
					        	if(largeLen==0)
					        		return false;
					        	if(smallLen==0)
					        		return true;
					        	  // If last characters of two strings are matching
					        	if(large.charAt(largeLen-1)==small.charAt(smallLen-1))
					        		isSubSequence(large, small, largeLen-1, smallLen-1);
					        	// If last characters are not matching
					        	return isSubSequence(large, small, largeLen-1, smallLen);
					        }
					     
					        // To Get Input
					         	// Some Buffer Methods
					         
					         	public static void InputReader(InputStream stream1) {
					         		stream = stream1;
					         	}
					         
					         	private static boolean isWhitespace(int c) {
					         		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
					         	}
					         
					         	private static boolean isEndOfLine(int c) {
					         		return c == '\n' || c == '\r' || c == -1;
					         	}
					         
					         	private static int read() {
					         		if (numChars == -1)
					         			throw new InputMismatchException();
					         		if (curChar >= numChars) {
					         			curChar = 0;
					         			try {
					         				numChars = stream.read(buf);
					         			} catch (IOException e) {
					         				throw new InputMismatchException();
					         			}
					         			if (numChars <= 0)
					         				return -1;
					         		}
					         		return buf[curChar++];
					         	}
					         
					         	private static int nextInt() {
					         		int c = read();
					         		while (isSpaceChar(c))
					         			c = read();
					         		int sgn = 1;
					         		if (c == '-') {
					         			sgn = -1;
					         			c = read();
					         		}
					         		int res = 0;
					         		do {
					         			if (c < '0' || c > '9')
					         				throw new InputMismatchException();
					         			res *= 10;
					         			res += c - '0';
					         			c = read();
					         		} while (!isSpaceChar(c));
					         		return res * sgn;
					         	}
					          
					         	private static long nextLong() {
					         		int c = read();
					         		while (isSpaceChar(c))
					         			c = read();
					         		int sgn = 1;
					         		if (c == '-') {
					         			sgn = -1;
					         			c = read();
					         		}
					         		long res = 0;
					         		do {
					         			if (c < '0' || c > '9')
					         				throw new InputMismatchException();
					         			res *= 10;
					         			res += c - '0';
					         			c = read();
					         		} while (!isSpaceChar(c));
					         		return res * sgn;
					         	}
					          
					         	private static String nextToken() {
					         		int c = read();
					         		while (isSpaceChar(c))
					         			c = read();
					         		StringBuilder res = new StringBuilder();
					         		do {
					         			res.appendCodePoint(c);
					         			c = read();
					         		} while (!isSpaceChar(c));
					         		return res.toString();
					         	}
					          
					         	private static String nextLine() {
					         		int c = read();
					         		while (isSpaceChar(c))
					         			c = read();
					         		StringBuilder res = new StringBuilder();
					         		do {
					         			res.appendCodePoint(c);
					         			c = read();
					         		} while (!isEndOfLine(c));
					         		return res.toString();
					         	}
					         
					         	private static int[] nextIntArray(int n) {
					         		int[] arr = new int[n];
					         		for (int i = 0; i < n; i++) {
					         			arr[i] = nextInt();
					         		}
					         		return arr;
					         	}
					         	  
					         	private static long[] nextLongArray(int n) {
					         		long[] arr = new long[n];
					         		for (int i = 0; i < n; i++) {
					         			arr[i] = nextLong();
					         		}
					         		return arr;
					         	}
					         
					         	private static void pArray(int[] arr){
					         		for (int i=0; i<arr.length; i++) {
					         			System.out.print(arr[i] + " ");
					         		}
					         		System.out.println();
					         		return;
					         	}
					         
					         	private static void pArray(long[] arr){
					         		for (int i=0; i<arr.length; i++) {
					         			System.out.print(arr[i] + " ");
					         		}
					         		System.out.println();
					         		return;		
					         	}
					         	
					         	private static void pArray(boolean[] arr){
					         		for (int i=0; i<arr.length; i++) {
					         			System.out.print(arr[i] + " ");
					         		}
					         		System.out.println();
					         		return;
					         	}
					     
					         
					         	private static boolean isSpaceChar(int c) {
					         		if (filter != null)
					         			return filter.isSpaceChar(c);
					         		return isWhitespace(c);
					         	}
					          
					         	private interface SpaceCharFilter {
					         		public boolean isSpaceChar(int ch);
					         	}
					         	
					         	private static void multiply(int a[][], int b[][])
					         	{
					         	    // Creating an auxiliary matrix to store elements 
					         	    // of the multiplication matrix
					         	    int mul[][]=new int[2][2];
					         	    for (int i = 0; i <2; i++)
					         	    {
					         	        for (int j = 0; j < 2; j++)
					         	        {
					         	            mul[i][j] = 0;
					         	            for (int k = 0; k < 2; k++)
					         	                mul[i][j] += a[i][k]*b[k][j];
					         	        }
					         	    }
					         	 
					         	    // storing the muliplication resul in a[][]
					         	    for (int i=0; i<2; i++)
					         	        for (int j=0; j<2; j++)
					         	            a[i][j] = mul[i][j];  // Updating our matrix
					         	}
					         	 
					         	// Function to compute F raise to power n-2.
					         	private static int power(int F[][], long n)
					         	{
					         	    int M[][]={{1,1},{1,0}};
					         	 
					         	    // Multiply it with initial values i.e with
					         	    // F(0) = 0, F(1) = 1, F(2) = 1
					         	    if (n==1)
					         	        return F[0][0] + F[0][1];
					         	 
					         	    power(F, n/2);
					         	 
					         	    multiply(F, F);
					         	 
					         	    if (n%2 != 0)
					         	        multiply(F, M);
					         	 
					         	    // Multiply it with initial values i.e with
					         	    // F(0) = 0, F(1) = 1, F(2) = 1
					         	    return F[0][0] + F[0][1] ;
					         	}
					         	 
					         	// Return n'th term of a series defined using below
					         	// recurrence relation.
					         	// f(n) is defined as
		//			         	    f(n) = f(n-1) + f(n-2) + f(n-3), n>=3
					         	// Base Cases :
		//			         	    f(0) = 0, f(1) = 1, f(2) = 1
					         private static long	 findNthTerm(long n)
					         	{
					        	 
					         	    int F[][] = {{1,1}, {1,0}} ;
					         	 
					         	    return power(F, n-2);
					         	}
					         	private static int GetRightPosition(int A[], int l, int r, int key)
					         	{
					         	    int m;
					         	 
					         	    while( r - l > 1 )
					         	    {
					         	        m = l + (r - l)/2;
					         	 
					         	        if( A[m] <= key )
					         	            l = m;
					         	        else
					         	            r = m;
					         	    }
					         	 
					         	    return l;
					         	}
					         	 
					         	private static int GetLeftPosition(int A[], int l, int r, int key)
					         	{
					         	    int m;
					         	 
					         	    while( r - l > 1 )
					         	    {
					         	        m = l + (r - l)/2;
					         	 
					         	        if( A[m] >= key )
					         	            r = m;
					         	        else
					         	            l = m;
					         	    }
					         	 
					         	    return r;
					         	}
					         	 
					         	private static int CountOccurances(int A[], int size, int key)
					         	{
					         	    // Observe boundary conditions
					         	    int left = GetLeftPosition(A, -1, size-1, key);
					         	    int right = GetRightPosition(A, 0, size, key);
					         	 
					         	    // What if the element doesn't exists in the array?
					         	    // The checks helps to trace that element exists
					         	    return (A[left] == key && key == A[right])?
					         	           (right - left + 1) : 0;
					         	}
					         	private static int Ceil(int a[],int low,int high,int target){
					         		if(target<=a[low]){
					         			return a[low];
					         			
					         		}
					         		if(target>a[high])
					         			return -1;
					         		while(high-low>1){
					         			int mid=low+(high-low)/2;
					         			if(a[mid]<target){
					         				low=mid;
					         				if(mid+1<=a.length-1 && a[mid+1]>=target)
					         					return a[mid+1];
					         			}
					         			if(a[mid]>=target){
					         				high=mid;
					         				if(mid-1>=0 && a[mid-1]<target){
					         					return a[mid];
					         				}
					         			}
					         		}
					         		return -1;
					         	}
			
					         	private static int floor(int a[],int low,int high,int target){
					         		if(target<a[low]){
					         			return -1;
					         		}
					         		if(target>=a[high])
					         			return a[high];
					         		while(high-low>1)
					         		{
					         			int mid=low+(high-low)/2;
					         		if(a[mid]>target){
					         			high=mid;
					         			if(mid-1>=0 && a[mid-1]<=target){
					         				return a[mid-1];
					         			}
					         		}
					         		if(a[mid]<=target){
					         			low=mid;
					         			if((mid+1)<=a.length-1 && a[mid+1]>target){
					         				return a[mid];
					         			}
					         		}
					         			
					         		}
					         		return -1;
					         	}
					         	private static int BinarySearch(int a[],int low,int high,int target){
					         	if(low>high)
					         		return -1;
					         	int mid=low+(high-low)/2;
					         	if(a[mid]==target)
					         		return mid;
					         	if(a[mid]>target)
					         		high=mid-1;
					         	if(a[mid]<target)
					         		low=mid+1;
					         		return BinarySearch(a, low, high, target);
					         	}
					         //	-----------------------My Code-----------------------------------------
					         	 private static void soln(){
					         		int n=nextInt();
					         	int a[]=nextIntArray(n);
					         	HashMap<Integer,Integer> hm=new HashMap<>();
					         	int ind=0;
					         	if(n==1){
					         		System.out.println(0);
					         		System.out.println(a[0]);
					         		System.exit(0);
					         	}
					         	hm.put(ind, a[0]);
					         	ind++;
					         	for(int i=0;i<n-1;i++){
					         		if(gcd(a[i], a[i+1])!=1){
					         			
					         			hm.put(ind,1);
					         			ind++;
					         			hm.put(ind, a[i+1]);
					         			ind++;
					         		}else{
					         			//System.out.println(ind);
					         			hm.put(ind, a[i+1]);
					         			ind++;
					         		}
					         	}
					         	System.out.println(hm.size()-n);
					         	for(int i=0;i<ind;i++){
					         		System.out.print(hm.get(i)+" ");
					         	}
					         		
					        }
					        
					       
					        
					         	}
					        class MyComp implements Comparator<Integer>{

								@Override
								public int compare(Integer o1, Integer o2) {
									if(o1<o2){
										return 1;
									}else if(o1>o2){
										return -1;
									}
									return 0;
								}

								
					        	
					        }
					        class Graph{
					        	private long conse=0,co=0,mac_cons_cat=0;
					        	private int V,flag=1, d[], road_cond[][];
					        	private Stack <Integer>st=new Stack();
					        	private LinkedList<Integer > adj[];
					        	private HashMap<String ,Integer> hs =new HashMap<>();
					        //	boolean Visited[];
					        	Graph(int V){
					        		V++;
					        
					        		
					        		//this.mac_cons_cat=max_cat;
					        		this.V=(V);
					        		adj=new LinkedList[V];
					        		//for(int i=0;i<V;i++)
					        			//adj[i]=new LinkedList();
					        		
					        			
					        		//Visited=new boolean[V];
					        	 
					        	}
					        	void addEdge(int v,int w,int t){
					        		if(adj[v]==null){
					        			adj[v]=new LinkedList();
					        		}
					        		adj[v].add(w);
					        		String temp="";
					        		temp+=v;
					        		temp+=w;
					        		//System.out.println(temp+"---");
					        		if(!hs.containsKey(temp))
					        		hs.put(temp, t);
					        	
					        	}
					        	public long  bfs(int s)
					            {
					        		co=0;
					                // Mark all the vertices as not visited(By default
					                // set as false)
					                boolean visited[] = new boolean[V];
					         
					                // Create a queue for BFS
					                LinkedList<Integer> queue = new LinkedList<Integer>();
					         
					                // Mark the current node as visited and enqueue it
					                visited[s]=true;
					                queue.add(s);
					         
					                while (queue.size() != 0)
					                {
					                    // Dequeue a vertex from queue and print it
					                    s = queue.poll();
					                   // System.out.print(s+" ");
					         
					                    // Get all adjacent vertices of the dequeued vertex s
					                    // If a adjacent has not been visited, then mark it
					                    // visited and enqueue it
					                    Iterator<Integer> i = adj[s].listIterator();
					                    while (i.hasNext())
					                    {
					                        int n = i.next();
					                        if (!visited[n])
					                        {
					                            visited[n] = true;
					                            queue.add(n);
					                        co++;
					                        }
					                    }
					                    return co;
					                }
					                return 0;
					            }
					        	 public long  dfs(int startVertex){
					        		
					        		boolean Visited[]=new boolean[V];
					        		
					        		//flag=1;
					        		
					        		 if(!Visited[startVertex])  {
					        			
					        			 co=0; 
					        			 dfsUtil(startVertex,Visited);
					           		 
					        		 }
					        		 
					        		 return co;
					        	 }
					        	 public void Connected(int v){
					        		 Iterator<Integer> i = adj[v].listIterator();
					        		 while(i.hasNext()){
					        			 int n=i.next();
					        			 long data=(long)d[n]+(long)d[v];
					        			 data=data%1000000007;
					        			 d[n]=(int)data;
					        		 }
					        	 }
					        	 public int getByte(int v){
					        		 return d[v];
					        	 }
					        	private void dfsUtil(int startVertex, boolean[] Visited) {
					        		//System.out.println(pre+" "+startVertex);
					        		
					        		Visited[startVertex]=true;
					        		
					        		
					        		st.push(startVertex);
					        		while(!st.isEmpty()){
					        			int top=st.pop();
					        			System.out.print(top+" ");
					        			
					        			//System.out.println(top);
					        		Iterator<Integer> i=adj[top].listIterator();
					        	
					        		while(i.hasNext()){
					        			int n=i.next();
					        		//	System.out.println(n+"---");
					        			 if( !Visited[n]){
					        				Visited[n]=true;
					        					st.push(n);
					        					co++;
					        					}
					        			 }
					        		
					        	}
					        		}
					        }
					
					        class Dsu{
					        	private int rank[], parent[] ,n;
					        	
					        	Dsu(int size){
					        		this.n=size+1;
					        		rank=new int[n];
					        		parent=new int[n];
					        	makeSet();
					        	}
					        	
					        	void makeSet(){
					        		for(int i=0;i<n;i++){
					        			parent[i]=i;
					        		}
					        	}
					        	
					        	int find(int x){
					        		if(parent[x]!=x){
					        			
					        			parent[x]=find(parent[x]);
					        		}
					        		return parent[x];
					        	}	
					        	
					        	void union(int x,int y){
					        		int xRoot=find(x);
					        		int yRoot=find(y);
					        		
					        		if(xRoot==yRoot)
					        			return;
					        		if(rank[xRoot]<rank[yRoot]){
					        		parent[xRoot]=yRoot;	
					        		}else if(rank[yRoot]<rank[xRoot]){
					        			parent[yRoot]=xRoot;
					        		}else{
					        			parent[yRoot]=xRoot;
					        			rank[xRoot]++;
					        		}
					        		
					        	}
					        }