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.BufferedReader;
import java.io.Closeable;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.StringTokenizer;

public class A {
	
	public static long gcd(long a, long b){
		return b == 0 ? a : gcd(b, a % b);
	}
	
	public static void main(String[] args) {
		try (final Scanner sc = new Scanner(System.in)) {
			
			final int n = sc.nextInt();
			long[] arr = new long[n];
			
			for(int i = 0; i < n; i++){
				arr[i] = sc.nextLong();
			}
			
			StringBuilder sb = new StringBuilder();
			int count = 0;
			for(int i = 0; i < n; i++){
				final long fst = arr[i];
				if(i == n - 1){ sb.append((i == 0 ? "" : " ") + fst); continue; }
				
				final long snd = arr[i + 1];
				
				final long gcd = gcd(fst, snd);
				if(gcd == 1){ // co-priem
					sb.append((i == 0 ? "" : " ") + fst);
				}else{ // no-coprime
					count++;
					long co_prime = 2;
					for(co_prime = 2; (gcd(fst, co_prime) != 1|| gcd(snd, co_prime) != 1); co_prime++){}
					
					sb.append((i == 0 ? "" : " ") + fst + " " + (co_prime));
				}
			}
			
			
			
			System.out.println(count);
			System.out.println(sb.toString());
		}
	}
	
	public static class Scanner implements Closeable {
		private BufferedReader br;
		private StringTokenizer tok;

		public Scanner(InputStream is) {
			br = new BufferedReader(new InputStreamReader(is));
		}

		private void getLine() {
			try {
				while (!hasNext()) {
					tok = new StringTokenizer(br.readLine());
				}
			} catch (IOException e) { /* ignore */
			}
		}

		private boolean hasNext() {
			return tok != null && tok.hasMoreTokens();
		}

		public String next() {
			getLine();
			return tok.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}
		
		public long nextLong() {
			return Long.parseLong(next());
		}

		public void close() {
			try {
				br.close();
			} catch (IOException e) { /* ignore */
			}
		}
	}
}