Problem: The problem uses a simplified TCP/IP address model, please read the statement carefully.

An IP address is a 32-bit integer, represented as a group of four decimal 8-bit integers (without leading zeroes), separated by commas. For example, record 0.255.1.123 shows a correct IP address and records 0.256.1.123 and 0.255.1.01 do not. In the given problem an arbitrary group of four 8-bit integers is a correct IP address.

Our hero Polycarpus still works as a system administrator in some large corporation. He likes beautiful IP addresses. To check if some IP address is beautiful, he should do the following:

  1. write out in a line four 8-bit numbers of the IP address, without the commas; 
  2. check if the resulting string is a palindrome. 



Let us remind you that a palindrome is a string that reads the same from right to left and from left to right.

For example, IP addresses 12.102.20.121 and 0.3.14.130 are beautiful (as strings "1210220121" and "0314130" are palindromes), and IP addresses 1.20.20.1 and 100.4.4.1 are not.

Polycarpus wants to find all beautiful IP addresses that have the given set of digits. Each digit from the set must occur in the IP address at least once. IP address must not contain any other digits. Help him to cope with this difficult task.

Input

The first line contains a single integer n (1 ≤ n ≤ 10) — the number of digits in the set. The second line contains the set of integers a1, a2, ..., an (0 ≤ ai ≤ 9). It is guaranteed that all digits in the set are distinct.

Output

In the first line print a single integer k — the number of beautiful IP addresses that contain the given set of digits. In the following k lines print the IP addresses, one per line in the arbitrary order.

Examples

Input

6
0 1 2 9 8 7


Output

6
78.190.209.187
79.180.208.197
87.190.209.178
89.170.207.198
97.180.208.179
98.170.207.189


Input

1
4


Output

16
4.4.4.4
4.4.4.44
4.4.44.4
4.4.44.44
4.44.4.4
4.44.4.44
4.44.44.4
4.44.44.44
44.4.4.4
44.4.4.44
44.4.44.4
44.4.44.44
44.44.4.4
44.44.4.44
44.44.44.4
44.44.44.44

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.BufferedWriter;
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.Arrays;
import java.util.HashSet;
import java.util.List;
import java.util.StringTokenizer;


public class CROCRound1TaskC implements Runnable {

	private void tryIt(int a, int b) {
		String str = a + "" + b;
		int size = str.length();
		for (int i = 0; i < size; ++i) {
			tryIt(a, b, str.substring(0, i), str.substring(i));
		}
	}
	
	private String rev(String s) {
		sb.setLength(0);
		for (int i = s.length()-1; i >= 0; --i) {
			sb.append(s.charAt(i));
		}
		return sb.toString();
	}
	
	private void tryIt(int a, int b, String center, String left) {
		String r = rev(left);
		int size = left.length();
		for (int point = 1; point < size; ++point) {
			String a1 = r.substring(0, point);
			String b1 = r.substring(point, size);
			if (correct(r.substring(0, point)) && correct(r.substring(point, size))) {
				String s = a1 + "" + b1 + a + b;
				if (s.compareTo(rev(s)) == 0 && ok(s)) {
					ips.add(a1.concat(".").concat(b1).concat("." + a + "." + b));
				}
			}
		}
	}
	
	private void tryIt2(int a, int b) {
		String str = a + "" + b;
		int size = str.length();
		for (int i = 0; i < size; ++i) {
			tryIt(str.substring(0, i), str.substring(i), a, b);
		}
	}
	
	private void tryIt(String right, String center, int a, int b) {
		String r = rev(right);
		int size = right.length();
		for (int point = 1; point < size; ++point) {
			String a1 = r.substring(0, point);
			String b1 = r.substring(point, size);
			if (correct(r.substring(0, point)) && correct(r.substring(point, size))) {
				String s = a + "" + b + a1 + b1;
				if (s.compareTo(rev(s)) == 0 && ok(s)) {
					ips.add((a + "." + b + ".").concat(a1.concat(".").concat(b1)));
				}
			}
		}
	}
	
	private boolean ok(String str) {
		++timer;
		for (int i = 0; i < str.length(); ++i) {
			lastVisit[str.charAt(i) - 48] = timer;
		}
		for (int i = 0; i < 10; ++i) {
			if (digits[i] && lastVisit[i] < timer ||
			    !digits[i] && lastVisit[i] == timer) {
				return false;
			}
		}
		return true;
	}
	
	private boolean correct(String str) {
		return (str.charAt(0) != '0' || str.length() == 1) && (str.length() < 3 || str.length() == 3 && str.compareTo("256") < 0);
	}
	
	private HashSet<String> ips;
	
	private StringBuilder sb;
	
	private void solve(PrintWriter out) {
		sb = new StringBuilder();
		ips = new HashSet<String>();
		for (int i = 0; i < 256; ++i) {
			for (int j = 0; j < 256; ++j) {
				tryIt(i, j);
			}
		}
		for (int i = 0; i < 256; ++i) {
			for (int j = 0; j < 256; ++j) {
				tryIt2(i, j);
			}
		}
		out.println(ips.size());
		for (String ip: ips) {
			out.println(ip);
		}
	}
	
	private void readData() {
		InputReader in = new InputReader(System.in);
		n = in.readInt();
		digits = new boolean[10];
		lastVisit = new int[10];
		timer = 0;
		Arrays.fill(lastVisit, 0);
		Arrays.fill(digits, false);
		for (int i = 0; i < n; ++i) {
			digits[in.readInt()] = true;
		}
	}
	
	private int n;
	private boolean[] digits;
	private int[] lastVisit;
	private int timer;
	
	@Override
	public void run() {
		readData();
		PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		solve(out);
		out.flush();
	}	
	
	public static void main(String[] args) {
		new CROCRound1TaskC().run();
	}
	
	private class InputReader {
		
	    public BufferedReader reader;
	    public StringTokenizer tokenizer;

	    public InputReader(InputStream stream) {
	        reader = new BufferedReader(new InputStreamReader(stream));
	        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 readInt() {
	    	return Integer.parseInt(next());
	    }
	    
	    
	}

}