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:
/**
 * Built using VSCode,Custom Python and Bash files
 * @author Siddhraj Sisodiya
 */

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

public class Main 
{
   public static void main(String[] args)
    {
        OutputWriter out = new OutputWriter(new PrintWriter(System.out));
        Task solver = new Task();
        solver.solve(new InputReader(System.in),out);
        out.close();
    }
}
class Task
{
    Merge merge;
    Task()
    {
        merge=new Merge();
    }
    public void solve(InputReader in,OutputWriter out)
    {
        int a=in.nextInt(),b=in.nextInt(),c=in.nextInt(),d=in.nextInt();
        char ans[][]=new char[50][50];
        for(int i=0;i<50;i++)
        {
            Arrays.fill(ans[i],'-');
        }
        Pair flower[]=new Pair[4];
        flower[0]=new Pair('A', a);
        flower[1]=new Pair('B', b);
        flower[2]=new Pair('C', c);
        flower[3]=new Pair('D', d);
        Arrays.sort(flower);
        int max=0;
        int temp=1;
        char fillerChar=flower[0].s;
        flower[3].l--;
        flower[0].l--;
        for(int i=3;i>=0;i--)
        {
            int count=0;
            Pair current=flower[i];
            int currentValue=current.l;
            char currentkey=current.s;
            int j=temp;
            while(count<48&&currentValue>0)
            {
                ans[j][count+1]=currentkey;
                currentValue--;
                count++;
                if(count%2==1)
                {
                    j++;
                }
                else{
                    j--;
                }
            }
            if(count>max)
            {
                max=count;
            }
            for(int iti=temp-1;iti<=temp+2;iti++)
            {
                for(int itj=0;itj<max+2;itj++)
                {
                    if(ans[iti][itj]=='-')
                    {
                        ans[iti][itj]=fillerChar;
                    }
                }
            }
            temp=temp+4;
            if(currentValue!=0)
            {
                flower[i].l=currentValue;
                i++;
                continue;
            }
            if(i==3)
            {
                fillerChar=flower[3].s;
            }
        }
        out.prints(temp-1);
        out.println(max+2);
        for(int iti=0;iti<temp-1;iti++)
        {
            for(int itj=0;itj<max+2;itj++)
            {
                if(ans[iti][itj]=='-')
                {
                        ans[iti][itj]=flower[0].s;
                }
            }
        }
        for(int i=0;i<temp-1;i++)
        {
            for(int j=0;j<max+2;j++)
            {
                out.print(ans[i][j]);
            }
            out.println("");
        }
    }
    /* here out is inbuild function keep in mind
     * never use float as no inbuild function for that
     * out.printf() is as slow as system.out.print()
     * long x=30L;
     */
}

class Merge
{
    public void sort(int a[])
    {
        ArrayList<Integer> arr=new ArrayList<>();
        for(int i=0;i<a.length;i++)
        {
            arr.add(a[i]);
        }
        Collections.sort(arr);
        for(int i=0;i<a.length;i++)
        {
            a[i]=arr.get(i);
        }
    }
    public void sort(long a[])
    {
        ArrayList<Long> arr=new ArrayList<>();
        for(int i=0;i<a.length;i++)
        {
            arr.add(a[i]);
        }
        Collections.sort(arr);
        for(int i=0;i<a.length;i++)
        {
            a[i]=arr.get(i);
        }
    }
    public void sort(double a[])
    {
        ArrayList<Double> arr=new ArrayList<>();
        for(int i=0;i<a.length;i++)
        {
            arr.add(a[i]);
        }
        Collections.sort(arr);
        for(int i=0;i<a.length;i++)
        {
            a[i]=arr.get(i);
        }
    }
}

class Pair implements Comparable<Pair>
{
     char s;
     Integer l;
    Pair(char s,int l)
    {
        this.s=s;
        this.l=l;
    
    }
    public int compareTo(Pair p)
    {
        return Integer.compare(this.l,p.l);
    }
    
}

class OutputWriter
{
    StringBuilder line;
    PrintWriter out;
    public OutputWriter(PrintWriter out)
    {
        this.out=out;
        line=new StringBuilder();
    }
    public void print(int n)
    {
        line.append(n);
    }
    public void prints(int n)
    {
        line.append(n).append(' ');
    }
    public void println(int n)
    {
        line.append(n).append('\n');
    }
    public void print(long n)
    {
        line.append(n);
    }
    public void prints(long n)
    {
        line.append(n).append(' ');
    }
    public void println(long n)
    {
        line.append(n).append('\n');
    }
    public void print(double n)
    {
        line.append(n);
    }
    public void prints(double n)
    {
        line.append(n).append(' ');
    }
    public void println(double n)
    {
        line.append(n).append('\n');
    }
    public void print(String n)
    {
        line.append(n);
    }
    public void prints(String n)
    {
        line.append(n).append(' ');
    }
    public void println(String n)
    {
        line.append(n).append('\n');
    }
    public void print(char n)
    {
        line.append(n);
    }
    public void prints(char n)
    {
        line.append(n).append(' ');
    }
    public void println(char n)
    {
        line.append(n).append('\n');
    }
    public void printf(String str,Object... o)
    {
        line.append(String.format(str, o));
    }
    public void close()
    {
        out.print(line);
        out.flush();
    }
}

class InputReader
{
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    public InputReader(InputStream stream)
    {
        this.stream = stream;
    }
    public int[] nextIntArray(int n)
    {
        int[] ret = new int[n];
        for (int i = 0; i < n; i++)
        {
            ret[i] = nextInt();
        }
        return ret;
    }
    public int[][] nextIntTable(int n, int m)
    {
        int[][] ret = new int[n][m];
        for (int i = 0; i < n; i++)
        {
            for (int j = 0; j < m; j++)
            {
                ret[i][j] = nextInt();
            }
        }
        return ret;
    }
    public long[] nextLongArray(int n)
    {
        long[] ret = new long[n];
        for (int i = 0; i < n; i++)
        {
            ret[i] = nextLong();
        }
        return ret;
    }
    public long[][] nextLongTable(int n, int m)
    {
        long[][] ret = new long[n][m];
        for (int i = 0; i < n; i++)
        {
            for (int j = 0; j < m; j++)
            {
                ret[i][j] = nextLong();
            }
        }
        return ret;
    }
    public double[] nextDoubleArray(int n)
    {
        double[] ret = new double[n];
        for (int i = 0; i < n; i++)
        {
            ret[i] = nextDouble();
        }
        return ret;
    }
    public int next()
    {
        if (numChars == -1)
            throw new InputMismatchException();
        if (curChar >= numChars)
        {
            curChar = 0;
            try
            {
                numChars = stream.read(buf);
            }
            catch (IOException e)
            {
                throw new InputMismatchException();
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }
    public char nextChar()
    {
        int c = next();
        while (isSpaceChar(c))
            c = next();
        if ('a' <= c && c <= 'z')
        {
            return (char) c;
        }
        if ('A' <= c && c <= 'Z')
        {
            return (char) c;
        }
        throw new InputMismatchException();
    }
    public String nextToken()
    {
        int c = next();
        while (isSpaceChar(c))
            c = next();
        StringBuilder res = new StringBuilder();
        do
        {
            res.append((char) c);
            c = next();
        }
        while (!isSpaceChar(c));
        return res.toString();
    }
    public int nextInt()
    {
        int c = next();
        while (isSpaceChar(c))
            c = next();
        int sgn = 1;
        if (c == '-')
        {
            sgn = -1;
            c = next();
        }
        int res = 0;
        do
        {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c-'0';
            c = next();
        }
        while (!isSpaceChar(c));
        return res*sgn;
    }
    public long nextLong()
    {
        int c = next();
        while (isSpaceChar(c))
            c = next();
        long sgn = 1;
        if (c == '-')
        {
            sgn = -1;
            c = next();
        }
        long res = 0;
        do
        {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c-'0';
            c = next();
        }
        while (!isSpaceChar(c));
        return res*sgn;
    }
    public double nextDouble()
    {
        return Double.valueOf(nextToken());
    }
    public boolean isSpaceChar(int c)
    {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }
    public interface SpaceCharFilter
    {
        public boolean isSpaceChar(int ch);
    }
}