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.util.*;
 
public class Main {
     
    public static StreamTokenizer in;   
    static double nextNumber() throws IOException {
        in.nextToken();
        return in.nval;
    }
    static String nextStr() throws IOException {
        in.nextToken();
        return in.sval;
    }
    static int gcd(int a, int b) {
    	BigInteger ans = BigInteger.valueOf(a).gcd(BigInteger.valueOf(b));
    	return ans.intValue();
    }
    static Random rand = new Random();
    public static void main(String args[]) throws IOException {
    	in = new StreamTokenizer(new BufferedReader(new InputStreamReader(System.in)));     
//    	Scanner in = new Scanner(System.in); 
//    	in = new StreamTokenizer(new FileReader("point.in"));
//    	Scanner in = new Scanner(new FileReader("intput.in"));
    	PrintWriter out = new PrintWriter(System.out);
//    	PrintWriter out = new PrintWriter(new FileWriter("point.out")); 
    	int n = (int)nextNumber();
    	int[] a = new int[n];
    	for(int i=0;i<n;i++) {
    		int x = (int)nextNumber();
    		a[i]=x;
    	}
    	int count = 0;
    	for(int i=1;i<n;i++) {
    		int x = a[i];
    		int y = a[i-1];
    		if(gcd(x, y)!=1) {
    			count++;
    		}
    	}
    	System.out.println(count);
    	System.out.print(a[0]+" ");
    	for(int i=1;i<n;i++) {
    		int x = a[i];
    		int y = a[i-1];
    		int r =0;
    		if(gcd(x, y)!=1) {
    			System.out.print(1+" ");
    		}
    		System.out.print(a[i]+" ");
    	}
    }    
}