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.awt.CardLayout;
import java.awt.Color;
import java.awt.Component;
import java.awt.Container;
import java.awt.Dimension;
import java.awt.FileDialog;
import java.awt.LayoutManager;
import java.awt.event.KeyEvent;
import java.awt.event.KeyListener;
import java.awt.font.NumericShaper;
import java.awt.image.BufferedImage;
import java.io.InputStreamReader;
import java.io.IOException;
import java.text.DecimalFormat;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Hashtable;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;
import java.util.Set;
import java.util.Stack;
import java.util.TreeSet;
import javax.imageio.ImageIO;
import javax.swing.ImageIcon;
import javax.swing.JButton;
import javax.swing.JFrame;
import javax.swing.JLabel;
import java.io.BufferedReader;
import java.io.File;
import java.io.FilenameFilter;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.util.Timer;
import java.util.TimerTask;
import java.io.InputStream;
import java.lang.reflect.Array;
import java.math.BigDecimal;
import java.math.BigInteger;

public class palin {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(System.out);
		TaskC solver = new TaskC();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskC {
	public void solve(int testNumber, InputReader in, PrintWriter out) {
		boolean prime[] = new boolean[1000];
		Arrays.fill(prime, true);
		prime[0] = prime[1] = false;
		for (int i = 2; i < prime.length; i++) {
			if (prime[i]) {
				for (int j = 2 * i; j < prime.length; j += i) {
					prime[j] = false;
				}
			}
		}
		int n = in.nextInt(), a[] = new int[n];
		for (int i = 0; i < a.length; i++) {
			a[i] = in.nextInt();
		}
		int count = 0;
		for (int i = 0; i < a.length - 1; i++) {
			if (gcd(a[i], a[i + 1]) != 1) {
				count++;
			}
		}
		System.out.println(count);
		for (int i = 0; i < a.length - 1; i++) {
			System.out.print(a[i] + " ");
			if (gcd(a[i], a[i + 1]) != 1) {
				for (int j = 0; j < prime.length; j++) {
					if (prime[j] && gcd(j, a[i]) == 1 && gcd(j, a[i + 1]) == 1) {
						System.out.print(j + " ");
						break;
					}
				}
			}
		}
		System.out.println(a[n - 1]);
	}

	int gcd(int a, int b) {
		int temp = b;
		b = a % b;
		a = temp;
		if (b == 0) {
			return a;
		}
		return gcd(a, b);
	}
}

class InputReader {
	BufferedReader br;
	StringTokenizer st;

	public InputReader(InputStream in) {
		br = new BufferedReader(new InputStreamReader(in));
		st = null;
	}

	public String next() {
		while (st == null || !st.hasMoreTokens()) {
			try {
				st = new StringTokenizer(br.readLine());
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		return st.nextToken();
	}

	public int nextInt() {
		return Integer.parseInt(next());
	}

	public long nextLong() {
		return Long.parseLong(next());
	}

	public float nextFloat() {
		return Float.parseFloat(next());
	}

	public double nextDouble() {
		return Double.parseDouble(next());
	}
}