Three companies decided to order a billboard with pictures of their logos. A billboard is a big square board. A logo of each company is a rectangle of a non-zero area. 

Advertisers will put up the ad only if it is possible to place all three logos on the billboard so that they do not overlap and the billboard has no empty space left. When you put a logo on the billboard, you should rotate it so that the sides were parallel to the sides of the billboard.

Your task is to determine if it is possible to put the logos of all the three companies on some square billboard without breaking any of the described rules.

Input

The first line of the input contains six positive integers x1, y1, x2, y2, x3, y3 (1 ≤ x1, y1, x2, y2, x3, y3 ≤ 100), where xi and yi determine the length and width of the logo of the i-th company respectively.

Output

If it is impossible to place all the three logos on a square shield, print a single integer "-1" (without the quotes).

If it is possible, print in the first line the length of a side of square n, where you can place all the three logos. Each of the next n lines should contain n uppercase English letters "A", "B" or "C". The sets of the same letters should form solid rectangles, provided that:

  * the sizes of the rectangle composed from letters "A" should be equal to the sizes of the logo of the first company, 
  * the sizes of the rectangle composed from letters "B" should be equal to the sizes of the logo of the second company, 
  * the sizes of the rectangle composed from letters "C" should be equal to the sizes of the logo of the third company, 



Note that the logos of the companies can be rotated for printing on the billboard. The billboard mustn't have any empty space. If a square billboard can be filled with the logos in multiple ways, you are allowed to print any of them.

See the samples to better understand the statement.

Examples

Input

5 1 2 5 5 2


Output

5
AAAAA
BBBBB
BBBBB
CCCCC
CCCCC


Input

4 4 2 6 4 2


Output

6
BBBBBB
BBBBBB
AAAACC
AAAACC
AAAACC
AAAACC

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 D_Round_322_Div2 {

    public static long MOD = 1000000007;

    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();
        Point[] data = new Point[3];
        int total = 0;
        for (int i = 0; i < 3; i++) {
            data[i] = new Point(in.nextInt(), in.nextInt());
            total += data[i].x * data[i].y;
        }
        int n = isSquare(total);
        if (n == -1) {
            out.println(-1);
        } else {
            //System.out.println(n);
            boolean found = false;
            int[] pre = {0, 1, 2};
            do {

                for (int i = 0; i < (1 << 3); i++) {
                    char[][] re = order(pre, i, n, data);
                    if (re != null) {
                        found = true;
                        out.println(n);
                        for (int j = 0; j < n; j++) {
                            for (int k = 0; k < n; k++) {
                                out.print(re[j][k]);
                            }
                            out.println();
                        }
                        break;
                    }
                }
            } while (nextPer(pre) && !found);
            if (!found) {
                out.println(-1);
            }
        }
        out.close();
    }

    static char[][] order(int[] pre, int mask, int n, Point[] data) {
        char[][] result = new char[n][n];
        boolean[][] mark = new boolean[n][n];
        // System.out.println("HE HE");
        for (int i = 0; i < 3; i++) {
            boolean found = false;
            for (int k = 0; k < n && !found; k++) {
                for (int h = 0; h < n; h++) {
                    if (!mark[k][h]) {
//						System.out.println(Arrays.toString(pre) + " "
//								+ Integer.toBinaryString(mask) + " " + k + " "
//								+ h + " " + pre[i]);
                        if (((1 << pre[i]) & mask) == 0) {
                            for (int p = 0; p < data[pre[i]].x; p++) {
                                for (int q = 0; q < data[pre[i]].y; q++) {
                                    if (k + p >= n || q + h >= n || mark[k + p][q + h]) {
                                        return null;
                                    }
                                    mark[k + p][q + h] = true;
                                    result[k + p][q + h] = (char) (pre[i] + 'A');
                                }
                            }
                        } else {
                            for (int p = 0; p < data[pre[i]].y; p++) {
                                for (int q = 0; q < data[pre[i]].x; q++) {
                                    if (k + p >= n || q + h >= n  || mark[k + p][q + h]) {
                                        return null;
                                    }
                                    mark[k + p][q + h] = true;
                                    result[k + p][q + h] = (char) (pre[i] + 'A');
                                }
                            }
                        }
//						for (char[] c : result) {
//							System.out.println(Arrays.toString(c));
//						}
                        found = true;
                        break;
                    }

                }
            }

        }
     //   System.out.println(Arrays.toString(pre) + " " + Integer.toBinaryString(mask));
        return result;
    }

    static int isSquare(int v) {
        for (int i = 1; i * i <= v; i++) {
            if (i * i == v) {
                return i;
            }
        }
        return -1;
    }

    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();
            }
        }
    }
}
