Problem: Vasya has a multiset s consisting of n integer numbers. Vasya calls some number x nice if it appears in the multiset exactly once. For example, multiset \{1, 1, 2, 3, 3, 3, 4\} contains nice numbers 2 and 4.

Vasya wants to split multiset s into two multisets a and b (one of which may be empty) in such a way that the quantity of nice numbers in multiset a would be the same as the quantity of nice numbers in multiset b (the quantity of numbers to appear exactly once in multiset a and the quantity of numbers to appear exactly once in multiset b).

Input

The first line contains a single integer n~(2 ≤ n ≤ 100).

The second line contains n integers s_1, s_2, ... s_n~(1 ≤ s_i ≤ 100) — the multiset s.

Output

If there exists no split of s to satisfy the given requirements, then print "NO" in the first line.

Otherwise print "YES" in the first line.

The second line should contain a string, consisting of n characters. i-th character should be equal to 'A' if the i-th element of multiset s goes to multiset a and 'B' if if the i-th element of multiset s goes to multiset b. Elements are numbered from 1 to n in the order they are given in the input.

If there exist multiple solutions, then print any of them.

Examples

Input

4
3 5 7 1


Output

YES
BABA


Input

3
3 5 1


Output

NO

Solution (in JAVA):

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

public class Main

{ 
	 static FastReader sc=new FastReader(); 
	 static int dp[][];
	 static int mod=1000000007;
	 
	  public static void main(String[] args)  throws IOException
{
		    //CHECK FOR N=1
       	//CHECK FOR N=1
	    //CHECK FOR N=1			
       	//CHECK FOR N=1
		   PrintWriter out=new PrintWriter(System.out);
		   StringBuffer sb=new StringBuffer("");
		  int ttt=1;
		  // ttt =i(); 			 
		   
		   
	        outer :while (ttt-- > 0) 
			{
	        	int n=i();
	        	int A[]=input(n);
	        	HashMap<Integer,Integer> map=hash(A);
	        	int c=0;
	        	int d=0;
	        	for(int k : map.keySet()) {
	        		if(map.get(k)>2) {
	        			d++;
	        		}
	        		if(map.get(k)==1)
	        			c++;
	        	}
	        	if(c%2==0) {
	        		System.out.println("YES");
	        		c/=2;
	        		for(int i=0;i<n;i++) {
	        			if(map.get(A[i])==1) {
	        				if(c>0) {
	        					System.out.print('B');
	        					c--;
	        				}
	        				else {
	        					System.out.print('A');
	        				}
	        			}
	        			else {
	        				System.out.print('A');
	        			}
	        		}
	        		return;
	        	}
	        	else {
	        		if(d>0) {
	        			c/=2;
	        			System.out.println("YES");
	        			int g=1;
	        			for(int i=0;i<n;i++) {
	        				if(map.get(A[i])==1) {
		        				if(c>0) {
		        					System.out.print('B');
		        					c--;
		        				}
		        				else {
		        					System.out.print('A');
		        				}
		        			}
		        			else {
		        				if(map.get(A[i])>2) {
		        					if(g>0) {
			        					System.out.print('B');
			        					g--;
			        				}
			        				else {
			        					System.out.print('A');
			        				}	
		        				}
		        				else {
		        					System.out.print('A');
		        				}
		        			}
	        			}
	        			
	        			return;
	        		}
	        	}
	        	System.out.println("NO");
			}
		 
		     out.close();
    	//System.out.println(sb.toString());
	     
	     
	    //CHECK FOR N=1                    //CHECK FOR M=0
        //CHECK FOR N=1                    //CHECK FOR M=0
       	//CHECK FOR N=1
       	//CHECK FOR N=1
       	//CHECK FOR N=1
		        	
    }
	  public static String[] permutationOfString(String input){
			// Write your code here
	        if(input.length()<=1)
	        {
	            String ans[]={input};
	            return ans;
	        }
	        String small[]=permutationOfString(input.substring(1));
	        String ans[]=new String[(small.length)*(input.length())];
	        int k=0;
	        for(int i=0;i<small.length;i++){
	            StringBuffer ob=new StringBuffer(small[i]);
	            for(int j=0;j<=(small[i].length());j++){
	                ans[k]=new String(ob.insert(j,input.charAt(0)));
	                k++;
	                ob=new StringBuffer(small[i]);
	            }
	        }
	            
	        return ans;
	  }
	  
	  
static int[] input(int n) {
	int A[]=new int[n];
	   for(int i=0;i<n;i++) {
		   A[i]=sc.nextInt();
	   }
	   return A;
   }
static long[] inputL(int n) {
	long A[]=new long[n];
	   for(int i=0;i<n;i++) {
		   A[i]=sc.nextLong();
	   }
	   return A;
   }
static String[] inputS(int n) {
	String A[]=new String[n];
	   for(int i=0;i<n;i++) {
		   A[i]=sc.next();
	   }
	   return A;
   }
static long sum(int A[]) {
	long sum=0;
	for(int i : A) {
		sum+=i;
	}
	return sum;
}
static long sum(long A[]) {
	long sum=0;
	for(long i : A) {
		sum+=i;
	}
	return sum;
}

static void input(int A[],int B[]) {
	   for(int i=0;i<A.length;i++) {
		   A[i]=sc.nextInt();
		   B[i]=sc.nextInt();
	   }
}
static int[][] input(int n,int m){
	int A[][]=new int[n][m];
	for(int i=0;i<n;i++) {
		for(int j=0;j<m;j++) {
			A[i][j]=i();
		}
	}
	return A;
}
static char[][] charinput(int n,int m){
	char A[][]=new char[n][m];
	for(int i=0;i<n;i++) {
		String s=s();
		for(int j=0;j<m;j++) {
			A[i][j]=s.charAt(j);
		}
	}
	return A;
}
static int max(int A[]) {
	int max=Integer.MIN_VALUE;
	for(int i=0;i<A.length;i++) {
		max=Math.max(max, A[i]);
	}
	return max;
}
static int min(int A[]) {
	int min=Integer.MAX_VALUE;
	for(int i=0;i<A.length;i++) {
		min=Math.min(min, A[i]);
	}
	return min;
}
static long max(long A[]) {
	long max=Long.MIN_VALUE;
	for(int i=0;i<A.length;i++) {
		max=Math.max(max, A[i]);
	}
	return max;
}
static long min(long A[]) {
	long min=Long.MAX_VALUE;
	for(int i=0;i<A.length;i++) {
		min=Math.min(min, A[i]);
	}
	return min;
}
static long mod(long x) {
	 int mod=1000000007;
	  return ((x%mod + mod)%mod);
}
static String reverse(String s) {
	StringBuffer p=new StringBuffer(s);
	p.reverse();
	return p.toString();
}

     static int i() {
    	 return sc.nextInt();
     }
     static String s() {
    	 return sc.next();
     }
     static long l() {
    	 return sc.nextLong();
     }  
     static void sort(int[] A){
        int n = A.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i){
            int tmp = A[i];
            int randomPos = i + rnd.nextInt(n-i);
            A[i] = A[randomPos];
            A[randomPos] = tmp;
        }
        Arrays.sort(A);
     }
     static void sort(long[] A){
	        int n = A.length;
	        Random rnd = new Random();
	        for(int i=0; i<n; ++i){
	            long tmp = A[i];
	            int randomPos = i + rnd.nextInt(n-i);
	            A[i] = A[randomPos];
	            A[randomPos] = tmp;
	        }
	        Arrays.sort(A);
	     }
  static String sort(String s) {
 	 Character ch[]=new Character[s.length()];
 	 for(int i=0;i<s.length();i++) {
 		 ch[i]=s.charAt(i);
 	 }
 	 Arrays.sort(ch);
 	 StringBuffer st=new StringBuffer("");
 	 for(int i=0;i<s.length();i++) {
 		 st.append(ch[i]);
 	 }
 	 return st.toString();
  }
  static HashMap<Integer,Integer> hash(int A[]){
	  HashMap<Integer,Integer> map=new HashMap<Integer, Integer>();
	  for(int i : A) {
		  if(map.containsKey(i)) {
			  map.put(i, map.get(i)+1);
		  }
		  else {
			  map.put(i, 1);
		  }
	  }
	  return map;
  }
  static TreeMap<Integer,Integer> tree(int A[]){
	  TreeMap<Integer,Integer> map=new TreeMap<Integer, Integer>();
	  for(int i : A) {
		  if(map.containsKey(i)) {
			  map.put(i, map.get(i)+1);
		  }
		  else {
			  map.put(i, 1);
		  }
	  }
	  return map;
  }
     static boolean prime(int n) 
	    { 
	        if (n <= 1) 
	            return false; 
	        if (n <= 3) 
	            return true; 
	        if (n % 2 == 0 || n % 3 == 0) 
	            return false; 
	        double sq=Math.sqrt(n);
	  
	        for (int i = 5; i <= sq; i = i + 6) 
	            if (n % i == 0 || n % (i + 2) == 0) 
	                return false; 
	        return true; 
	    } 
     static boolean prime(long n) 
	    { 
	        if (n <= 1) 
	            return false; 
	        if (n <= 3) 
	            return true; 
	        if (n % 2 == 0 || n % 3 == 0) 
	            return false; 
	        double sq=Math.sqrt(n);
	  
	        for (int i = 5; i <= sq; i = i + 6) 
	            if (n % i == 0 || n % (i + 2) == 0) 
	                return false; 
	        return true; 
	    } 
     static int gcd(int a, int b) 
     { 
         if (a == 0) 
             return b; 
         return gcd(b % a, a); 
     } 
     static long gcd(long a, long b) 
     { 
         if (a == 0) 
             return b; 
         return gcd(b % a, a); 
     } 
     static class Pair implements Comparable<Pair>
     {
    	 int x;
    	 int y;
    	 Pair(int x,int y){
    		 this.x=x;
    		 this.y=y;
    	 }
		@Override
		public int compareTo(Pair o) {
			if(this.x>o.x)
				return 1;
			else if(this.x<o.x)
				return -1;
			else {
				if(this.y>o.y)
					return 1;
				else if(this.y<o.y)
					return -1;
				else
					return 0;
			}
		}
     }
        
    static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    } 
}