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:
/* Codeforces Template */

import java.io.*;
import java.util.*;

import static java.lang.Math.*;
import static java.util.Arrays.fill;
import static java.util.Arrays.binarySearch;
import static java.util.Arrays.sort;

public class Main {
	
	static long initTime;
	static final Random rnd = new Random(7777L);
	static boolean writeLog = false;
	
	public static void main(String[] args) throws IOException {
		initTime = System.currentTimeMillis();
		try {
			writeLog = "true".equals(System.getProperty("LOCAL_RUN_7777"));
		} catch (SecurityException e) {}
		new Thread(null, new Runnable() {
			public void run() {
				try {
					try {
						if (new File("input.txt").exists())
							System.setIn(new FileInputStream("input.txt"));
					} catch (SecurityException e) {}
					long prevTime = System.currentTimeMillis();
					new Main().run();
					log("Total time: " + (System.currentTimeMillis() - prevTime) + " ms");
					log("Memory status: " + memoryStatus());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
		}, "1", 1L << 24).start(); 
	}

	void run() throws IOException {
		in = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);
		solve();
		out.close();
		in.close();
	}
	
	/*************************************************************** 
	 * Solution
	 **************************************************************/

	int n;
	int[] ds;

	int len;
	
	List<String> answer = new ArrayList<String>();
	
	void solve() throws IOException  {
		
		n = nextInt();
		ds = nextIntArray(n);
		
		for (len = 4; len <= 12; len++) {
			rec(0);
		}
		
		out.println(answer.size());
		for (String s : answer)
			out.println(s);
	}
	
	int[] ip = new int [12];
	int[] used = new int [10];
	
	void rec(int pos) {

		int restDigits = (len + 1) >> 1;
		int restUnused = 0;
		
		for (int i = 0; i < n; i++)
			if (used[i] == 0)
				restUnused++;
		if (restUnused > restDigits)
			return;
		
		if (pos + pos >= len) {
			updateAnswer();
			return;
		}
		
		for (int i = 0; i < n; i++) {
			ip[pos] = ds[i];
			used[i]++;
			rec(pos + 1);
			used[i]--;
		}
		
	}

	void updateAnswer() {
		
		for (int i = 0; i < n; i++)
			if (used[i] == 0)
				return;
		
		for (int i = 0; i + i < len; i++) {
			ip[len - 1 - i] = ip[i];
		}
		
//		System.err.println(Arrays.toString(Arrays.copyOf(ip, len)));
		
		print(0, 0);
		
	}
	
	int[] cuts = new int [4];

	void print(int pos, int block) {
		int restBlocks = 4 - block;
		int restDigits = len - pos;
		if (3 * restBlocks < restDigits || restDigits < restBlocks) return;
		
		if (block == 3) {
			if (isValidCut(pos, restDigits))
				answer.add(getIp());
			return;
		}
		
		for (int cut = 1; cut <= 3; cut++) {
			if (isValidCut(pos, cut)) {
				cuts[block] = cut;
				print(pos + cut, block + 1);
			}
		}
	}

	final StringBuilder sb = new StringBuilder();
	
	String getIp() {
		sb.setLength(0);
		int k = 0;
		for (int i = 0; i < 3; i++) {
			for (int j = 0; j < cuts[i]; j++)
				sb.append(ip[k++]);
			sb.append('.');
		}
		while (k < len)
			sb.append(ip[k++]);
		return sb.toString();
	}

	final int[] minNum = { -1, 0, 10, 100 };
	final int[] maxNum = { -1, 9, 99, 255 };
	
	boolean isValidCut(int pos, int len) {
		int x = getNumber(pos, len);
		return minNum[len] <= x && x <= maxNum[len];
	}
	
	final int[] pow = { 1, 10, 100 };

	int getNumber(int pos, int len) {
		int ret = 0;
		for (int i = 0; i < len; i++)
			ret += pow[len - 1 - i] * ip[pos + i];
		return ret;
	}

	/*************************************************************** 
	 * Input 
	 **************************************************************/
	BufferedReader in;
	PrintWriter out;
	StringTokenizer st = new StringTokenizer("");
	
	String nextToken() throws IOException {
		while (!st.hasMoreTokens())
			st = new StringTokenizer(in.readLine());
		return st.nextToken();
	}
	
	int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}
	
	long nextLong() throws IOException {
		return Long.parseLong(nextToken());
	}
	
	double nextDouble() throws IOException {
		return Double.parseDouble(nextToken());
	}
	
	int[] nextIntArray(int size) throws IOException {
		int[] ret = new int [size];
		for (int i = 0; i < size; i++)
			ret[i] = nextInt();
		return ret;
	}
	
	long[] nextLongArray(int size) throws IOException {
		long[] ret = new long [size];
		for (int i = 0; i < size; i++)
			ret[i] = nextLong();
		return ret;
	}
	
	double[] nextDoubleArray(int size) throws IOException {
		double[] ret = new double [size];
		for (int i = 0; i < size; i++)
			ret[i] = nextDouble();
		return ret;
	}
	
	String nextLine() throws IOException {
		st = new StringTokenizer("");
		return in.readLine();
	}
	
	boolean EOF() throws IOException {
		while (!st.hasMoreTokens()) {
			String s = in.readLine();
			if (s == null)
				return true;
			st = new StringTokenizer(s);
		}
		return false;
	}
	
	/*************************************************************** 
	 * Output 
	 **************************************************************/
	void printRepeat(String s, int count) {
		for (int i = 0; i < count; i++)
			out.print(s);
	}
	
	void printArray(int[] array) {
		if (array == null || array.length == 0)
			return;
		for (int i = 0; i < array.length; i++) {
			if (i > 0) out.print(' ');
			out.print(array[i]);
		}
		out.println();
	}
	
	void printArray(long[] array) {
		if (array == null || array.length == 0)
			return;
		for (int i = 0; i < array.length; i++) {
			if (i > 0) out.print(' ');
			out.print(array[i]);
		}
		out.println();
	}
	
	void printArray(double[] array) {
		if (array == null || array.length == 0)
			return;
		for (int i = 0; i < array.length; i++) {
			if (i > 0) out.print(' ');
			out.print(array[i]);
		}
		out.println();
	}
	
	void printArray(double[] array, String spec) {
		if (array == null || array.length == 0)
			return;
		for (int i = 0; i < array.length; i++) {
			if (i > 0) out.print(' ');
			out.printf(Locale.US, spec, array[i]);
		}
		out.println();
	}
	
	void printArray(Object[] array) {
		if (array == null || array.length == 0)
			return;
		boolean blank = false;
		for (Object x : array) {
			if (blank) out.print(' '); else blank = true;
			out.print(x);
		}
		out.println();
	}
	
	@SuppressWarnings("rawtypes")
	void printCollection(Collection collection) {
		if (collection == null || collection.isEmpty())
			return;
		boolean blank = false;
		for (Object x : collection) {
			if (blank) out.print(' '); else blank = true;
			out.print(x);
		}
		out.println();
	}
	
	/*************************************************************** 
	 * Utility
	 **************************************************************/
	static String memoryStatus() {
		return (Runtime.getRuntime().totalMemory() - Runtime.getRuntime().freeMemory() >> 20) + "/" + (Runtime.getRuntime().totalMemory() >> 20) + " MB";
	}
	
	static void checkMemory() {
		System.err.println(memoryStatus());
	}
	
	static long prevTimeStamp = Long.MIN_VALUE;
	
	static void updateTimer() {
		prevTimeStamp = System.currentTimeMillis();
	}
	
	static long elapsedTime() {
		return (System.currentTimeMillis() - prevTimeStamp);
	}
	
	static void checkTimer() {
		System.err.println(elapsedTime() + " ms");
	}
	
	static void chk(boolean f) {
		if (!f) throw new RuntimeException("Assert failed");
	}
	
	static void chk(boolean f, String format, Object ... args) {
		if (!f) throw new RuntimeException(String.format(format, args));
	}
	
	static void log(String format, Object ... args) {
		if (writeLog) System.err.println(String.format(Locale.US, format, args));
	}
}