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.util.Arrays;
import java.util.Scanner;
import java.util.TreeMap;
import java.util.TreeSet;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.PrintWriter;
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.InputMismatchException;
import java.util.LinkedList;
import java.util.Map;
import java.util.PriorityQueue;

public class edu_1{
	public static void main(String args[]){
		FasterScanner s=new FasterScanner();
		PrintWriter out = new PrintWriter(System.out);
		int n=s.nextInt();
		int a[]=s.nextIntArray(n);
		ArrayList<Integer> al=new ArrayList<>();
		for(int i=0;i<n-1;i++){
			al.add(a[i]);
			if(gcd(a[i],a[i+1])!=1){
				al.add(1);
			}
		}
		al.add(a[n-1]);
		out.println(al.size()-n);
		for(int i=0;i<al.size();i++)
			out.print(al.get(i)+" ");
		out.close();
	}

	static class disjointSet {
		private int[] parent;  // parent[i] = parent of i
		private byte[] rank;   // rank[i] = rank of subtree rooted at i (never more than 31)
		private int count;     // number of components
		public disjointSet(int N) {
			if (N < 0) throw new IllegalArgumentException();
			count = N;
			parent = new int[N];
			rank = new byte[N];
			for (int i = 0; i < N; i++) {
				parent[i] = i;
				rank[i] = 0;
			}
		}
		public int find(int p) {
			if (p < 0 || p >= parent.length) throw new IndexOutOfBoundsException();
			while (p != parent[p]) {
				parent[p] = parent[parent[p]];    // path compression by halving
				p = parent[p];
			}
			return p;
		}
		public int[] p(){
			return parent;
		}
		public int count() {
			return count;
		}

		public boolean connected(int p, int q) {
			return find(p) == find(q);
		}

		public boolean union(int p, int q) {
			int rootP = find(p);
			int rootQ = find(q);
			if (rootP == rootQ) return false;

			// make root of smaller rank point to root of larger rank
			if      (rank[rootP] < rank[rootQ]) parent[rootP] = rootQ;
			else if (rank[rootP] > rank[rootQ]) parent[rootQ] = rootP;
			else {
				parent[rootQ] = rootP;
				rank[rootP]++;
			}
			count--;
			return true;
		}

	}
	static int gcd(int i,int j){
		if(i==0)
			return j;
		return gcd(j%i,i);
	}
	static class FasterScanner {
		private byte[] buf = new byte[1024];
		private int curChar;
		private int snumChars;
		public int read() {
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = System.in.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}
		public String nextLine() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndOfLine(c));
			return res.toString();
		}

		public String nextString() {
			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 long nextLong() {
			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 int nextInt() {
			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 int[] nextIntArray(int n) {
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextInt();
			}
			return arr;
		}

		public long[] nextLongArray(int n) {
			long[] arr = new long[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextLong();
			}
			return arr;
		}

		private boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		private boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}
	}
}