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.*;
import java.util.*;
import java.text.*;
import java.lang.*;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.util.regex.*;
import java.util.stream.LongStream;

public class Main{
	 //public static ArrayList a[]=new ArrayList[3000001];

	public static void main(String[] args)
   {
       InputReader in=new InputReader(System.in);
       PrintWriter pw = new PrintWriter(System.out);
       int x1=in.nextInt();
       int y1=in.nextInt();
       int x2=in.nextInt();
       int y2=in.nextInt();
       int x3=in.nextInt();
       int y3=in.nextInt();
       long a=(x1*y1)+(x2*y2)+(x3*y3);
       if(Math.floor((double)Math.sqrt(a))!=Math.ceil((double)Math.sqrt(a)))
    	   pw.println(-1);
       else
       {
    	   a=(long) Math.floor((double)Math.sqrt(a));
    	   char ans[][]=new char[(int) a][(int) a];
    	   boolean chk[]=new boolean [3];
    	   int st=0;
    	   if(x1==a || y1==a) {
    		   long rem=Math.min(x1, y1);
    		   for(int i=st;i<st+rem;i++) {
    			   for(int j=0;j<a;j++)
    				   ans[i][j]='A';
    		   }
    		   chk[0]=true;
    		   st+=rem;
    	   }
    	   if(x2==a || y2==a) {
    		   long rem=Math.min(x2, y2);
    		   for(int i=st;i<st+rem;i++) {
    			   for(int j=0;j<a;j++)
    				   ans[i][j]='B';
    		   }
    		   chk[1]=true;
    		   st+=rem;
    	   }
    	   if(x3==a || y3==a) {
    		   long rem=Math.min(x3, y3);
    		   for(int i=st;i<st+rem;i++) {
    			   for(int j=0;j<a;j++)
    				   ans[i][j]='C';
    		   }
    		   chk[2]=true;
    		   st+=rem;
    	   }
    	   
    	   int re=0;
    	   for(int i=0;i<3;i++) {
    		   if(!chk[i])
    			   re++;
    	   }
    	   if( re==3)
    		   pw.println(-1);
    	   else
    	   {
    		   int b[][]=new int[3][2];
    		   int start=0;
    		   b[0][0]=x1; b[0][1]=y1; b[1][0]=x2; b[1][1]=y2; b[2][0]=x3; b[2][1]=y3;
    		   int x=0;
    		   if(!chk[0] ) {
    			   if(x1==(a-st)|| y1==(a-st)){
    				   for(int i=st;i<a;i++) {
    					   	for(int j=x;j<x+((x1==(a-st))?y1:x1);j++) {
    					   		ans[i][j]='A';
    					   	}
    				   }
    				   x+=((x1==(a-st))?y1:x1);
    				   chk[0]=true;
    			   }
    		   }
    		   if(!chk[1] ) {
    			   if(x2==(a-st)|| y2==(a-st)){
    				   for(int i=st;i<a;i++) {
    					   	for(int j=x;j<x+((x2==(a-st))?y2:x2);j++) {
    					   		ans[i][j]='B';
    					   	}
    				   }
    				   x+=((x2==(a-st))?y2:x2);
    				   chk[1]=true;
    			   }
    		   }
    		   if(!chk[2] ) {
    			   if(x3==(a-st)|| y3==(a-st)){
    				   for(int i=st;i<a;i++) {
    					   	for(int j=x;j<x+((x3==(a-st))?y3:x3);j++) {
    					   		ans[i][j]='C';
    					   	}
    				   }
    				   x+=((x1==(a-st))?y3:x3);
    				   chk[2]=true;
    			   }
    		   }
    		   boolean fi=true;
    		   for(int i=0;i<3;i++) {
    			   fi&=chk[i];
    		   }
    		   if(fi) {
    			   pw.println(a);
    			   for(int i=0;i<a;i++) {
    				   for(int j=0;j<a;j++)
    					   pw.print(ans[i][j]);
    				   pw.println();
    			   }
    		   }
    		   else
    			   pw.println(-1);
    	   }
       }
       pw.flush();
       pw.close();
        
    }
         private static void debug(Object... o) {
     		System.out.println(Arrays.deepToString(o));
     	}
        static class InputReader 
        {
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;
 
        public InputReader(InputStream stream) 
        { 
            this.stream = stream;
        }
        public int snext() 
        {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) 
            {
                curChar = 0;
                try 
                {
                    snumChars = stream.read(buf);
                } 
                
                catch (IOException e) 
                {
                    throw new InputMismatchException();
                }
                
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
 
        public int nextInt() 
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = snext();
            }
            int res = 0;
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public long nextLong()
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-') 
            {
                sgn = -1;
                c = snext();
            }
            long res = 0;
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public int[] nextIntArray(int n) 
        {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) 
            {
                a[i] = nextInt();
            }
            return a;
        }
        static class tri implements Comparable<tri> {
            int p, c, l;
 
            tri(int p, int c, int l) {
                this.p = p;
                this.c = c;
                this.l = l;
            }
 
            public int compareTo(tri o) {
                return Integer.compare(l, o.l);
            }
        }
 
        public String readString()
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isSpaceChar(c));
            return res.toString();
        }
 
        public String nextLine() 
        {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isEndOfLine(c));
            return res.toString();
        }
 
        public boolean isSpaceChar(int c) 
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
        private boolean isEndOfLine(int c) 
        {
            return c == '\n' || c == '\r' || c == -1;
        }
 
        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
    }
        public static long mod = 1000000007;
        public static int d;
        public static int p;
        public static int q;
        
        public static int[] suffle(int[] a,Random gen)
        {
            int n = a.length;
            for(int i=0;i<n;i++)
            {
                int ind = gen.nextInt(n-i)+i;
                int temp = a[ind];
                a[ind] = a[i];
                a[i] = temp;
            }
            return a;
        }
        
        public static void swap(int a, int b){
            int temp = a;
            a = b;
            b = temp;
        }
        
       /* public static long primeFactorization(long n)
        {
             HashSet<Integer> a =new HashSet<Integer>();
        	long cnt=0;
            for(int i=2;i*i<=n;i++)
            {
                while(a%i==0)
                {
                    a.add(i);
                    a/=i;
                }
            }
            if(a!=1)
            	cnt++;
                //a.add(n);
            return cnt;
        }*/
        
        public static void sieve(boolean[] isPrime,int n)
        {
            for(int i=1;i<n;i++)
                isPrime[i] = true;
            
            isPrime[0] = false;
            isPrime[1] = false;
            
            for(int i=2;i*i<n;i++)
            {
                if(isPrime[i] == true)
                {
                    for(int j=(2*i);j<n;j+=i)
                        isPrime[j] = false;
                }
            }
        }
        
        public static int GCD(int a,int b)
        {
            if(b==0)
                return a;
            else
                return GCD(b,a%b);
        }
        
        public static long GCD(long a,long b)
        {
            if(b==0)
                return a;
            else
                return GCD(b,a%b);
        }
        
        public static void extendedEuclid(int A,int B)
        {
            if(B==0)
            {
                d = A;
                p = 1 ;
                q = 0;
            }
            else
            {
                extendedEuclid(B, A%B);
                int temp = p;
                p = q;
                q = temp - (A/B)*q;
            }
        }
        
        public static long LCM(long a,long b)
        {
            return (a*b)/GCD(a,b);
        }
        
        public static int LCM(int a,int b)
        {
            return (a*b)/GCD(a,b);
        }
        
        public static int binaryExponentiation(int x,int n)
        {
            int result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=result * x;
                x=x*x;
                n=n/2;
            }
            return result;
        }
        
        public static long binaryExponentiation(long x,long n)
        {
            long result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=result * x;
                x=x*x;
                n=n/2;
            }
            return result;
        }
        
        public static int modularExponentiation(int x,int n,int M)
        {
            int result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=(result * x)%M;
                x=(x%M*x)%M;
                n=n/2;
            }
            return result;
        }
        
        public static long modularExponentiation(long x,long n,long M)
        {
            long result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=(result%M * x%M)%M;
                x=(x%M * x%M)%M;
                n=n/2;
            }
            return result;
        }
        
        public static long modInverse(int A,int M)
        {
            return modularExponentiation(A,M-2,M);
        }
        
        public static long modInverse(long A,long M)
        {
            return modularExponentiation(A,M-2,M);
        }
        
        public static boolean isPrime(int n)
        {
            
            if (n <= 1)  return false;
            if (n <= 3)  return true;
            
            if (n%2 == 0 || n%3 == 0) 
                return false;
         
            for (int i=5; i*i<=n; i=i+6)
            {
                if (n%i == 0 || n%(i+2) == 0)
                   return false;
            }
            
            return true;
        }
        
         public static long[] shuffle(long[] a, Random gen){ 
                for(int i = 0, n = a.length;i < n;i++){ 
                    int ind = gen.nextInt(n-i)+i; 
                    long d = a[i]; 
                    a[i] = a[ind]; 
                    a[ind] = d; 
                } 
                return a; 
            }
         static class pair implements Comparable<pair>{
             Long x;
             Long y;
             pair(long l,long r){
                 this.x=l;
                 this.y=r;
             }
              public int compareTo(pair o) {
                     int result = x.compareTo(o.x);
                     if(result==0)
                         result = y.compareTo(o.y);
                     
                 return result;
                 }  
              public String toString(){
                 return (x+" "+y);
             }
       }       
 
      
}