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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.NoSuchElementException;
 
import java.util.*;
public class Main {
	int N;
	int[] a;
	public int gcd(int x,int y){
		return y == 0 ? x : gcd(y,x%y);
	}
	
	public void setPrime(){
		
	}
	
	public void solve(){
		N = nextInt();
		a = new int[N];
		for(int i = 0;i < N;i++){
			a[i] = nextInt();
		}
		ArrayList<Integer> ans = new ArrayList<Integer>();
		for(int i = 0;i < N - 1;i++){
			ans.add(a[i]);
			if(gcd(a[i],a[i + 1]) != 1){
				/*int max = Math.max(a[i],a[i + 1]);
				int min = Math.min(a[i],a[i + 1]);
				int[] yaku = new int[(int)(Math.sqrt(max)) + 2];
				for(int j = 2;j * j <= max;j++){
					if(yaku[j] > 0)continue;
					for(int k = 1;j * k <= max && max % (j * k) == 0;k++){
						yaku[j * k]++;
					}
				}
				int p = -1;
				for(int j = 2;j * j <= max;j++){
					if(yaku[j] == 0 && min % j != 0){
						p = j;
						break;
					}
				}*/
				ans.add(1);
			}
		}
		ans.add(a[N - 1]);
		out.println(ans.size() - N);
		for(int i = 0;i < ans.size();i++){
			if(i != 0){
				out.print(" ");
			}
			out.print(ans.get(i));
		}
	}
 
	public static void main(String[] args) {
		out.flush();
		new Main().solve();
		out.close();
	}
 
	/* Input */
	private static final InputStream in = System.in;
	private static final PrintWriter out = new PrintWriter(System.out);
	private final byte[] buffer = new byte[2048];
	private int p = 0;
	private int buflen = 0;
 
	private boolean hasNextByte() {
		if (p < buflen)
			return true;
		p = 0;
		try {
			buflen = in.read(buffer);
		} catch (IOException e) {
			e.printStackTrace();
		}
		if (buflen <= 0)
			return false;
		return true;
	}
 
	public boolean hasNext() {
		while (hasNextByte() && !isPrint(buffer[p])) {
			p++;
		}
		return hasNextByte();
	}
 
	private boolean isPrint(int ch) {
		if (ch >= '!' && ch <= '~')
			return true;
		return false;
	}
 
	private int nextByte() {
		if (!hasNextByte())
			return -1;
		return buffer[p++];
	}
 
	public String next() {
		if (!hasNext())
			throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = -1;
		while (isPrint((b = nextByte()))) {
			sb.appendCodePoint(b);
		}
		return sb.toString();
	}
 
	public int nextInt() {
		return Integer.parseInt(next());
	}
 
	public long nextLong() {
		return Long.parseLong(next());
	}
 
	public double nextDouble() {
		return Double.parseDouble(next());
	}
}