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.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.StringTokenizer;

public class CoPrimeArray implements Closeable {

    private InputReader in = new InputReader(System.in);
    private PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out), true);

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

    public void solve() {
        int n = in.ni();
        int[] list = new int[n];
        for (int i = 0; i < n; i++) {
            list[i] = in.ni();
        }
        List<Integer> result = new ArrayList<>();
        result.add(list[0]);
        int next = 1, last = result.get(0);
        while (next < n) {
            if (gcd(list[next], last) == 1) {
                result.add(list[next]);
            } else {
                for (int j = 2; ; j++) {
                    if (gcd(last, j) == 1 && gcd(list[next], j) == 1) {
                        result.add(j);
                        result.add(list[next]);
                        break;
                    }
                }
            }
            last = list[next];
            next++;
        }
        out.println(result.size() - list.length);
        for (Integer i : result) {
            out.print(i + " ");
        }
        out.println();
    }

    @Override
    public void close() throws IOException {
        in.close();
        out.close();
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

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

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

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

        public void close() throws IOException {
            reader.close();
        }
    }

    public static void main(String[] args) {
        new CoPrimeArray().solve();
    }
}