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.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Calendar;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.SortedSet;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

/**
 * #
 * @author pttrung
 */
public class C_CrocChamp2013_Round1 {

    public static long MOD = 1000000007;
    static ArrayList<StringBuilder>[][][][][]dp;
    public static void main(String[] args) throws FileNotFoundException {
        // PrintWriter out = new PrintWriter(new FileOutputStream(new File(
        // "output.txt")));
        PrintWriter out = new PrintWriter(System.out);
        Scanner in = new Scanner();
        int n = in.nextInt();

        int[] set = new int[10];
        Arrays.fill(set, -1);
        for (int i = 0; i < n; i++) {
            int v = in.nextInt();
            set[v] = i;
        }
        if (n > 6) {
            out.println(0);
        } else {
            dp = new ArrayList[2][1<<n][3][3][256];
            ArrayList<StringBuilder> result = cal(0, 0, 0, 0, 0, n, set);
            out.println(result.size());
            for (StringBuilder v : result) {
                out.println(v);
            }
        }
        out.close();
    }

    public static ArrayList<StringBuilder> cal(int index, int mask, int last, int need, int val, int n, int[] set) {
        if(dp[index][mask][last][need][val] != null){
            return dp[index][mask][last][need][val];
        }
        ArrayList<StringBuilder> result = new ArrayList();
        for (int i = 0; i < 256; i++) {
            if (check(i, set)) {
                for (int j = 0; j < 256; j++) {
                    if (check(j, set)) {
                        StringBuilder a = new StringBuilder();
                        a.append(i);
                        StringBuilder b = new StringBuilder();
                        b.append(j);
                        String v = "" + val;
                        if (last == 2) {
                            for (int k = 0; k < need; k++) {
                                b.append(v.charAt(k));
                            }
                        } else if (last == 1) {
                            a = a.reverse();
                            for (int k = v.length() - 1; k >= v.length() - need; k--) {
                                a.append(v.charAt(k));
                            }
                            a = a.reverse();
                        }
                        if (checkPalind(a, b, index == 1)) {

                            int nxt = calMask(mask, i, j, set);
                            if (index == 1) {
                                // System.out.println(Integer.bitCount(nxt) + " " + a + " " + b + " " + Integer.bitCount(mask));
                                if (Integer.bitCount(nxt) == n) {
                                    StringBuilder cur = new StringBuilder();
                                    cur.append(i).append(".").append(j);
                                    result.add(cur);
                                }
                            } else {
                                int nxtLast = a.length() == b.length() ? 0 : a.length() < b.length() ? 2 : 1;
                                int nxtNeed = Math.abs(a.length() - b.length());
                                int nxtVal = a.length() > b.length() ? i : j;

                                ArrayList<StringBuilder> tmp = cal(1, nxt, nxtLast, nxtNeed, nxtVal, n, set);

                                for (StringBuilder o : tmp) {
                                    StringBuilder cur = new StringBuilder();
                                    cur.append(i).append(".").append(o).append(".").append(j);
                                    result.add(cur);
                                }
                            }
                        }
                    }
                }
            }
        }
        return dp[index][mask][last][need][val] = result;
    }

    public static boolean checkPalind(StringBuilder a, StringBuilder b, boolean need) {
        if (need) {
            StringBuilder v = new StringBuilder(a);
            v.append(b);
            for (int i = 0; i < v.length() / 2; i++) {
                if (v.charAt(i) != v.charAt(v.length() - i - 1)) {
                    return false;
                }
            }
            return true;
        } else {
            for (int i = 0; i < Math.min(a.length(), b.length()); i++) {
                if (a.charAt(i) != b.charAt(b.length() - i - 1)) {
                    return false;
                }
            }
            return true;
        }
    }

    public static int calMask(int mask, int a, int b, int[] set) {
        if (a == 0) {
            mask |= (1 << set[0]);
        } else {
            while (a > 0) {
                mask |= (1 << set[a % 10]);
                a /= 10;
            }
        }
        if (b == 0) {
            mask |= (1 << set[0]);
        } else {
            while (b > 0) {
                mask |= (1 << set[b % 10]);
                b /= 10;
            }
        }
        return mask;
    }

    public static boolean check(int a, int[] set) {
        if (a == 0) {
            return set[0] != -1;
        }
        while (a > 0) {
            if (set[a % 10] == -1) {
                return false;
            }
            a /= 10;
        }
        return true;
    }

    public static int[] KMP(String val) {
        int i = 0;
        int j = -1;
        int[] result = new int[val.length() + 1];
        result[0] = -1;
        while (i < val.length()) {
            while (j >= 0 && val.charAt(j) != val.charAt(i)) {
                j = result[j];
            }
            j++;
            i++;
            result[i] = j;
        }
        return result;

    }

    public static boolean nextPer(int[] data) {
        int i = data.length - 1;
        while (i > 0 && data[i] < data[i - 1]) {
            i--;
        }
        if (i == 0) {
            return false;
        }
        int j = data.length - 1;
        while (data[j] < data[i - 1]) {
            j--;
        }
        int temp = data[i - 1];
        data[i - 1] = data[j];
        data[j] = temp;
        Arrays.sort(data, i, data.length);
        return true;
    }

    public static int digit(long n) {
        int result = 0;
        while (n > 0) {
            n /= 10;
            result++;
        }
        return result;
    }

    public static double dist(long a, long b, long x, long y) {
        double val = (b - a) * (b - a) + (x - y) * (x - y);
        val = Math.sqrt(val);
        double other = x * x + a * a;
        other = Math.sqrt(other);
        return val + other;

    }

    public static class Point implements Comparable<Point> {

        int x, y;

        public Point(int start, int end) {
            this.x = start;
            this.y = end;
        }

        @Override
        public int hashCode() {
            int hash = 5;
            hash = 47 * hash + this.x;
            hash = 47 * hash + this.y;
            return hash;
        }

        @Override
        public boolean equals(Object obj) {
            if (obj == null) {
                return false;
            }
            if (getClass() != obj.getClass()) {
                return false;
            }
            final Point other = (Point) obj;
            if (this.x != other.x) {
                return false;
            }
            if (this.y != other.y) {
                return false;
            }
            return true;
        }

        @Override
        public int compareTo(Point o) {
            return x - o.x;
        }
    }

    public static class FT {

        long[] data;

        FT(int n) {
            data = new long[n];
        }

        public void update(int index, long value) {
            while (index < data.length) {
                data[index] += value;
                index += (index & (-index));
            }
        }

        public long get(int index) {
            long result = 0;
            while (index > 0) {
                result += data[index];
                index -= (index & (-index));
            }
            return result;

        }
    }

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

    public static long pow(long a, long b, long MOD) {
        if (b == 0) {
            return 1;
        }
        if (b == 1) {
            return a;
        }
        long val = pow(a, b / 2, MOD);
        if (b % 2 == 0) {
            return val * val % MOD;
        } else {
            return val * (val * a % MOD) % MOD;

        }
    }

    static class Scanner {

        BufferedReader br;
        StringTokenizer st;

        public Scanner() throws FileNotFoundException {
            // System.setOut(new PrintStream(new BufferedOutputStream(System.out), true));
            br = new BufferedReader(new InputStreamReader(System.in));
            //  br = new BufferedReader(new InputStreamReader(new FileInputStream(new File("input.txt"))));
        }

        public String next() {

            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

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

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

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }

        public boolean endLine() {
            try {
                String next = br.readLine();
                while (next != null && next.trim().isEmpty()) {
                    next = br.readLine();
                }
                if (next == null) {
                    return true;
                }
                st = new StringTokenizer(next);
                return st.hasMoreTokens();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }
    }
}