Problem: As the boat drifts down the river, a wood full of blossoms shows up on the riverfront.

"I've been here once," Mino exclaims with delight, "it's breathtakingly amazing."

"What is it like?"

"Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?" 

There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses.

The wood can be represented by a rectangular grid of n rows and m columns. In each cell of the grid, there is exactly one type of flowers.

According to Mino, the numbers of connected components formed by each kind of flowers are a, b, c and d respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers.

You are to help Kanno depict such a grid of flowers, with n and m arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem.

Note that you can choose arbitrary n and m under the constraints below, they are not given in the input.

Input

The first and only line of input contains four space-separated integers a, b, c and d (1 ≤ a, b, c, d ≤ 100) — the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively.

Output

In the first line, output two space-separated integers n and m (1 ≤ n, m ≤ 50) — the number of rows and the number of columns in the grid respectively.

Then output n lines each consisting of m consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively.

In case there are multiple solutions, print any. You can output each letter in either case (upper or lower).

Examples

Input

5 3 2 1


Output

4 7
DDDDDDD
DABACAD
DBABACD
DDDDDDD

Input

50 50 1 1


Output

4 50
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
ABABABABABABABABABABABABABABABABABABABABABABABABAB
BABABABABABABABABABABABABABABABABABABABABABABABABA
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD

Input

1 6 4 5


Output

7 7
DDDDDDD
DDDBDBD
DDCDCDD
DBDADBD
DDCDCDD
DBDBDDD
DDDDDDD

Note

In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one.

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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_Round_487_Div2 {

    public static long MOD = 1000000007;
    static int i = 0;
    static int max = 0;

    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[] data = new int[4];
        for (int i = 0; i < 4; i++) {
            data[i] = in.nextInt();
        }
        int[][] re = new int[50][50];
        solve(0, 1, data[0], data[1], re);
        solve(2, 3, data[2], data[3], re);
        out.println((max + 1) + " " + 50);

        for (int k = 0; k <= max; k++) {
            for (int j : re[k]) {
                out.print((char) ('A' + j));
            }
            out.println();
        }
//        int[]v = count(re, max + 1);
//        out.println(Arrays.toString(v));
        out.close();
    }

    static void solve(int c, int d, int X, int Y, int[][] re) {
        int start = i;
        int[] tmp = {c, d};
        int[] s = {X, Y};
        for (; i < 50 && s[0] > 0 && s[1] > 0; i++) {
            for (int j = 0; j < 50; j++) {
                int nxt = -1;
                for (int k = 0; k < 2; k++) {
                    if (s[k] > 0) {
                        if (i == 0 || re[i - 1][j] != tmp[k]) {
                            if (j == 0 || re[i][j - 1] != tmp[k]) {
                                nxt = k;
                                break;
                            }
                        }
                    }
                }
                if (nxt == -1) {
                    if (i == start) {
                        for (int k = j; k < 50; k++) {
                            re[i][k] = re[i][j - 1];
                        }

                    } else {
                        re[i][j] = re[i - 1][j];
                        for (int k = j + 1; k < 50; k++) {
                            re[i][k] = re[i - 1][k];
                        }
                        if (re[i][j] == tmp[0]) {
                            s[0]++;
                        } else {
                            s[1]++;
                        }
                    }

                    max = i;
                    break;
                } else {
                    s[nxt]--;
                    re[i][j] = tmp[nxt];
                }
            }
            max = i;
        }
        //System.out.println(Arrays.toString(s) + " " + i);
        if (s[0] > 0) {
            fill(c, d, s[0], re);
        } else if (s[1] > 0) {
            fill(d, c, s[1], re);
        }

    }
    static int[] X = {0, 0, 1, -1};
    static int[] Y = {1, -1, 0, 0};

    static int[] count(int[][] re, int max) {
        int[] result = new int[4];
        boolean[][] check = new boolean[50][50];
        for (int k = 0; k < 4; k++) {
            for (int i = 0; i < max; i++) {
                for (int j = 0; j < 50; j++) {
                    if (!check[i][j] && re[i][j] == k) {
                        result[k]++;
                        LinkedList<Point> q = new LinkedList();
                        q.add(new Point(i, j));
                        check[i][j] = true;
                        while (!q.isEmpty()) {
                            Point p = q.poll();
                            for (int h = 0; h < 4; h++) {
                                int x = p.x + X[h];
                                int y = p.y + Y[h];
                                if (x >= 0 && x < max && y >= 0 && y < 50 && re[x][y] == k && !check[x][y]) {
                                    check[x][y] = true;
                                    q.add(new Point(x, y));
                                }
                            }
                        }
                    }
                }
            }
        }
        return result;
    }

    static void fill(int c, int d, int need, int[][] re) {
        int start;
        if (re[i - 1][0] == d) {
            re[i][0] = d;
            re[i][1] = d;
            start = 2;
        } else {
            re[i][0] = d;
            re[i][1] = d;
            re[i][2] = d;
            start = 3;
        }
        boolean first = true;
        boolean ok = true;
        for (int j = start; j < 50; j++) {

            re[i][j] = c;
            if (re[i - 1][j] == c && ok) {
                if (!first) {
                    need++;
                } else {
                    first = false;
                }
                ok = false;
            } else if (re[i - 1][j] == d) {
                ok = true;
            }

        }
        i++;
        for (int j = 0; j < 50; j++) {
            re[i][j] = d;
        }
        max = i;
        i++;
        for (; i < 50 && need > 0; i++) {

            for (int j = 0; j < 50; j++) {
                if (j % 2 == 0) {
                    re[i][j] = c;
                    need--;
                } else {
                    re[i][j] = d;
                }
                if (need == 0) {
                    for (int k = j + 1; k < 50; k++) {
                        re[i][k] = d;
                    }
                    break;
                }
            }
            i++;
            for (int j = 0; j < 50; j++) {
                re[i][j] = d;
            }
            max = i;
        }

    }

    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 Integer.compare(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();
            }
        }
    }
}