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.*;
import java.nio.charset.Charset;
import java.util.Arrays;
import java.util.Comparator;

public class Contest487C {
    public static void main(String[] args) throws FileNotFoundException {
        boolean local = System.getProperty("ONLINE_JUDGE") == null;
        IOUtil io;
        if (local) {
            io = new IOUtil(new FileInputStream("E:\\DATABASE\\TESTCASE\\codeforces\\Contest487C.in"), new FileOutputStream("E:\\DATABASE\\TESTCASE\\codeforces\\Contest487C.out"));
        } else {
            io = new IOUtil(System.in, System.out);
        }

        Task task = new Task(io);
        task.run();
        io.flush();
    }

    public static class Task implements Runnable {
        IOUtil io;

        public Task(IOUtil io) {
            this.io = io;
        }

        @Override
        public void run() {
            int[][] colors = new int[4][2];
            int[][] colors2 = new int[4][2];
            for (int i = 0; i < 4; i++) {
                colors[i][0] = 'A' + i;
                colors[i][1] = io.readInt();

                colors2[i] = colors[i].clone();
            }

            Arrays.sort(colors, new Comparator<int[]>() {
                @Override
                public int compare(int[] o1, int[] o2) {
                    return o1[1] - o2[1];
                }
            });


            char[][] map = new char[50][50];
            for (int i = 0; i < 50; i++) {
                Arrays.fill(map[i], (char) colors[0][0]);
            }
            colors[0][1]--;

            int r, c;
            for (r = 2; colors[0][1] > 0; r += 4) {
                for (c = 0; colors[0][1] > 0 && c < 48; c += 2) {
                    map[r + 1][c] = (char) pickUp(colors);
                    map[r][c + 1] = (char) pickUp(colors);
                    map[r - 1][c] = (char) pickUp(colors);
                    colors[0][1]--;
                }
            }

            r += 2;
            c = 0;
            int next;
            while ((next = pickUp(colors)) != -1) {
                map[r][c] = (char) next;
                c += 2;
                if (c == 50) {
                    c = 0;
                    r += 2;
                }
            }

            io.write(50);
            io.write(' ');
            io.write(50);
            io.write('\n');
            for (int i = 0; i < 50; i++) {
                io.write(String.valueOf(map[i]));
                io.write('\n');
            }
           // io.flush();

            boolean local = System.getProperty("ONLINE_JUDGE") == null;
            if (local) {
                int[][] components = new int[50][50];
                int[] total = new int[4];
                for (int i = 0; i < 50; i++) {
                    for (int j = 0; j < 50; j++) {
                        total[map[i][j] - 'A'] += dfs(components, map, i, j, map[i][j]);
                    }
                }

                for (int i = 0; i < 4; i++) {
                    if (colors2[i][1] != total[i]) {
                        throw new RuntimeException();
                    }
                }
            }



        }

        public static int dfs(int[][] comp, char[][] map, int i, int j, int color) {
            if (i < 0 || j < 0 || i >= 50 || j >= 50) {
                return 0;
            }

            if (comp[i][j] != 0 || map[i][j] != color) {
                return 0;
            }

            comp[i][j] = 1;
            dfs(comp, map, i + 1, j, color);
            dfs(comp, map, i - 1, j, color);
            dfs(comp, map, i, j + 1, color);
            dfs(comp, map, i, j - 1, color);

            return 1;
        }

        public static int pickUp(int[][] color) {
            for (int i = 1; i < 4; i++) {
                if (color[i][1] > 0) {
                    color[i][1]--;
                    return color[i][0];
                }
            }
            return -1;
        }
    }

    public static class IOUtil {
        private static int BUF_SIZE = 1 << 13;

        private byte[] r_buf = new byte[BUF_SIZE];
        private int r_cur;
        private int r_total;
        private int r_next;
        private final InputStream in;
        private StringBuilder temporary = new StringBuilder();

        StringBuilder w_buf = new StringBuilder();
        private final OutputStream out;

        public IOUtil(InputStream in, OutputStream out) {
            this.in = in;
            this.out = out;
        }

        private void skipBlank() {
            while (r_next <= 32) {
                r_next = read();
            }
        }

        public int readString(char[] data, int offset, int limit) {
            skipBlank();

            int originalLimit = limit;
            while (limit > 0 && r_next > 32) {
                data[offset++] = (char) r_next;
                limit--;
                r_next = read();
            }

            return originalLimit - limit;
        }

        public String readString(StringBuilder builder) {
            skipBlank();

            while (r_next > 32) {
                builder.append((char) r_next);
                r_next = read();
            }

            return builder.toString();
        }

        public String readString() {
            temporary.setLength(0);
            return readString(temporary);
        }

        public long readUnsignedLong() {
            skipBlank();

            long num = 0;
            while (r_next >= '0' && r_next <= '9') {
                num = num * 10 + r_next - '0';
                r_next = read();
            }
            return num;
        }

        public long readLong() {
            skipBlank();

            int sign = 1;
            while (r_next == '+' || r_next == '-') {
                if (r_next == '-') {
                    sign *= -1;
                }
                r_next = read();
            }

            return sign == 1 ? readUnsignedLong() : readNegativeLong();
        }

        public long readNegativeLong() {
            skipBlank();

            long num = 0;
            while (r_next >= '0' && r_next <= '9') {
                num = num * 10 - r_next + '0';
                r_next = read();
            }
            return num;
        }

        public int readUnsignedInt() {
            skipBlank();

            int num = 0;
            while (r_next >= '0' && r_next <= '9') {
                num = num * 10 + r_next - '0';
                r_next = read();
            }
            return num;
        }

        public int readNegativeInt() {
            skipBlank();

            int num = 0;
            while (r_next >= '0' && r_next <= '9') {
                num = num * 10 - r_next + '0';
                r_next = read();
            }
            return num;
        }

        public int readInt() {
            skipBlank();

            int sign = 1;
            while (r_next == '+' || r_next == '-') {
                if (r_next == '-') {
                    sign *= -1;
                }
                r_next = read();
            }

            return sign == 1 ? readUnsignedInt() : readNegativeInt();
        }

        public int read() {
            while (r_total <= r_cur) {
                try {
                    r_total = in.read(r_buf);
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
                r_cur = 0;
                if (r_total == -1) {
                    return -1;
                }
            }
            return r_buf[r_cur++];
        }

        public void write(char c) {
            w_buf.append(c);
        }

        public void write(int n) {
            w_buf.append(n);
        }

        public void write(String s) {
            w_buf.append(s);
        }

        public void write(long s) {
            w_buf.append(s);
        }

        public void write(double s) {
            w_buf.append(s);
        }

        public void write(float s) {
            w_buf.append(s);
        }

        public void write(Object s) {
            w_buf.append(s);
        }

        public void write(char[] data, int offset, int cnt) {
            for (int i = offset, until = offset + cnt; i < until; i++) {
                write(data[i]);
            }
        }

        public void flush() {
            try {
                out.write(w_buf.toString().getBytes(Charset.forName("ascii")));
                w_buf.setLength(0);
                out.flush();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }

        public double readDouble() {
            return Double.parseDouble(readString());
        }
    }
}