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.text.*;
import java.math.*;
import java.util.regex.*;
import java.lang.*;
public class Main{
	static long mod=1000000007;
//	static public HashMap<String,Integer> map=new HashMap<String,Integer>(); 
	//static public HashMap<Integer, String> map1=new HashMap<Integer,String>(); 

    public static void main(String[] args) throws Exception{           	
    	 InputReader in = new InputReader(System.in);       
    	PrintWriter pw=new PrintWriter(System.out); 
    	int prime[]=new int[1000001];
    	prime[0]=1;
    	prime[1]=1;
    int n=in.readInt();
    int a[]=new int[n];
    for(int i=0;i<n;i++)
    {
    	a[i]=in.readInt();
    }
    HashSet<Integer> set=new HashSet<Integer>();
    for(int i=0;i<1001;i++)
    {
    	if(prime[i]==0)
    		set.add(i);
    }
    HashMap<Integer,Integer> map=new HashMap<Integer,Integer>();
    for(int i=0;i<n-1;i++)
    {
    	if(gcd(a[i],a[i+1])==1)
    		continue;
    	else
    	{
    	for(int x:set)
    	{
    		if(gcd(x,a[i])==1&&gcd(x,a[i+1])==1)
    		{
    			map.put(i,x);
    			break;
    		}
    	}
    	}
    }
    System.out.println(map.size());
    for(int i=0;i<n;i++)
    {
    	if(!map.containsKey(i))
    	{
    		System.out.print(a[i]+ " ");
    	}
    	else
    		System.out.print(a[i]+" "+map.get(i)+" ");
    }
    
    }
	private static long count(long mid, int n, int m) {
	long c=0;
	for(int i=1;i<=n;i++)
	{
	c+=Math.min((long)m,(long)(mid-1)/(long)i);
	}
	return c;
}


	static class Pair implements Comparable<Pair>
	{
		int a;
		int b;
		@Override
		public int compareTo(Pair o) 
		{
			if(o.b>this.b) return 1;
			if(o.b<this.b) return -1;
			return 0;
		}
		
	}
public static int BinarySearch(long temp,long[] sum,int r)
{
	int l=0;
	
	while(l<=r)
	{
		int mid=l+(r-l)/2;
		if(sum[mid]==temp&&sum[mid]!=-1)
		{
		return mid;
		}
		if(sum[mid]>temp&&sum[mid]!=-1)
			r=mid-1;
		if(sum[mid]<temp&&sum[mid]!=-1)
			l=mid+1;
    }
	return -1;
}
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 int abs(int a,int b)
{
	return (int)Math.abs(a-b);
}
public static long abs(long a,long b)
{
	return (long)Math.abs(a-b);
}
public static int max(int a,int b)
{
	if(a>b)
		return a;
	else
		return b;
}
public static int min(int a,int b)
{
	if(a>b)
		return b;
	else 
		return a;
}
public static long max(long a,long b)
{
	if(a>b)
		return a;
	else
		return b;
}
public static long min(long a,long b)
{
	if(a>b)
		return b;
	else 
		return a;
}
 
 
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;
 
}

static long sort(int a[])
{  int n=a.length;
	int b[]=new int[n];	
	return mergeSort(a,b,0,n-1);}
static long mergeSort(int a[],int b[],long left,long right)
{ long c=0;if(left<right)
 {   long mid=left+(right-left)/2;
	 c= mergeSort(a,b,left,mid);
	 c+=mergeSort(a,b,mid+1,right);
	 c+=merge(a,b,left,mid+1,right); }	
	return c;	 }
static long merge(int a[],int  b[],long left,long mid,long right)
{long c=0;int i=(int)left;int j=(int)mid; int k=(int)left;
while(i<=(int)mid-1&&j<=(int)right)
{ if(a[i]<=a[j]) {b[k++]=a[i++]; }
else	{ b[k++]=a[j++];c+=mid-i;}}
while (i <= (int)mid - 1)   b[k++] = a[i++]; 
while (j <= (int)right) b[k++] = a[j++];
for (i=(int)left; i <= (int)right; i++) 
	a[i] = b[i];  return c;  }
    
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;
}    
   static  class InputReader
    {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
 
        public InputReader(InputStream stream)
        {
            this.stream = stream;
        }
 
        public 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++];
        }
 
        public int readInt()
        {
            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;
        }
 
        public String readString()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do
            {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }
        public double readDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, readInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, readInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }
        public long readLong() {
            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;
        }
        public boolean isSpaceChar(int c)
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
        public String next()
        {
            return readString();
        }
 
        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
    }
}