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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.Queue;


		    
		    
		    
		                                                public class Solution1 implements Runnable
		                                                {
		                                                    static final long MAX = 464897L;
		                                                    static class InputReader
		                                                    {
		                                                        private InputStream stream;
		                                                        private byte[] buf = new byte[1024];
		                                                        private int curChar;
		                                                        private int numChars;
		                                                        private SpaceCharFilter filter;
		                                                        private BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		                                                 
		                                                        public InputReader(InputStream stream)
		                                                        {
		                                                            this.stream = stream;
		                                                        }
		                                                        
		                                                        public int read()
		                                                        {
		                                                            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 String nextLine()
		                                                        {
		                                                            String str = "";
		                                                            try
		                                                            {
		                                                                str = br.readLine();
		                                                            }
		                                                            catch (IOException e)
		                                                            {
		                                                                e.printStackTrace();
		                                                            }
		                                                            return str;
		                                                        }
		                                                        public int nextInt()
		                                                        {
		                                                            int c = read();
		                                                            
		                                                            while(isSpaceChar(c)) 
		                                                                c = read();
		                                                            
		                                                            int sgn = 1;
		                                                            
		                                                            if (c == '-') 
		                                                            {
		                                                                sgn = -1;
		                                                                c = read();
		                                                            }
		                                                            
		                                                            int res = 0;
		                                                            do 
		                                                            {
		                                                                if(c<'0'||c>'9') 
		                                                                    throw new InputMismatchException();
		                                                                res *= 10;
		                                                                res += c - '0';
		                                                                c = read();
		                                                            }
		                                                            while (!isSpaceChar(c)); 
		                                                            
		                                                            return res * sgn;
		                                                        }
		                                                        
		                                                        public long nextLong() 
		                                                        {
		                                                            int c = read();
		                                                            while (isSpaceChar(c))
		                                                                c = read();
		                                                            int sgn = 1;
		                                                            if (c == '-') 
		                                                            {
		                                                                sgn = -1;
		                                                                c = read();
		                                                            }
		                                                            long res = 0;
		                                                            
		                                                            do 
		                                                            {
		                                                                if (c < '0' || c > '9')
		                                                                    throw new InputMismatchException();
		                                                                res *= 10;
		                                                                res += c - '0';
		                                                                c = read();
		                                                            }
		                                                            while (!isSpaceChar(c));
		                                                                return res * sgn;
		                                                        }
		                                                        
		                                                        public double nextDouble() 
		                                                        {
		                                                            int c = read();
		                                                            while (isSpaceChar(c))
		                                                                c = read();
		                                                            int sgn = 1;
		                                                            if (c == '-') 
		                                                            {
		                                                                sgn = -1;
		                                                                c = read();
		                                                            }
		                                                            double res = 0;
		                                                            while (!isSpaceChar(c) && c != '.') 
		                                                            {
		                                                                if (c == 'e' || c == 'E')
		                                                                    return res * Math.pow(10, nextInt());
		                                                                if (c < '0' || c > '9')
		                                                                    throw new InputMismatchException();
		                                                                res *= 10;
		                                                                res += c - '0';
		                                                                c = read();
		                                                            }
		                                                            if (c == '.') 
		                                                            {
		                                                                c = read();
		                                                                double m = 1;
		                                                                while (!isSpaceChar(c)) 
		                                                                {
		                                                                    if (c == 'e' || c == 'E')
		                                                                        return res * Math.pow(10, nextInt());
		                                                                    if (c < '0' || c > '9')
		                                                                        throw new InputMismatchException();
		                                                                    m /= 10;
		                                                                    res += (c - '0') * m;
		                                                                    c = read();
		                                                                }
		                                                            }
		                                                            return res * sgn;
		                                                        }
		                                                        
		                                                        public String readString() 
		                                                        {
		                                                            int c = read();
		                                                            while (isSpaceChar(c))
		                                                                c = read();
		                                                            StringBuilder res = new StringBuilder();
		                                                            do 
		                                                            {
		                                                                res.appendCodePoint(c);
		                                                                c = read();
		                                                            } 
		                                                            while (!isSpaceChar(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;
		                                                        }
		                                                     
		                                                        public String next() 
		                                                        {
		                                                            return readString();
		                                                        }
		                                                        
		                                                        public interface SpaceCharFilter 
		                                                        {
		                                                            public boolean isSpaceChar(int ch);
		                                                        }
		                                                    }
		                                                     
		                                                    public static void main(String args[]) throws Exception
		                                                    {
		                                                        new Thread(null, new Solution1(),"Solution",1<<26).start();
		                                                    }   
		                                                    static int gcd(int a, int b) 
		                                                    { 
		                                                      if (b == 0) 
		                                                        return a; 
		                                                      return gcd(b, a % b);  
		                                                    } 
		                                                    
		                                                    long MOD = 1000000007;
		                                                    
		                                                    ArrayList<Integer> adj[];
		                                                    ArrayList<Pair> adj2[];
		                                                    public void run() 
		                                                    {
		                                                        
		                                                            //InputReader sc= new InputReader(new FileInputStream("input.txt"));
		                                                            //PrintWriter w= new PrintWriter(new FileWriter("output.txt"));
		                                                            InputReader sc = new InputReader(System.in);
		                                                            PrintWriter w = new PrintWriter(System.out);
		                                                            int n = sc.nextInt();
		                                                            int[] arr = new int[n];
		                                                            char[] ch = new char[n];
		                                                            int[] freq=  new int[105];
		                                                            for(int i = 0;i < n;i++) {
		                                                            	arr[i] = sc.nextInt();
		                                                            	freq[arr[i]]++;
		                                                            }
		                                                            int c1 = 0;
		                                                            int c2 = 0;
		                                                            int rem = -1;
		                                                            for(int i = 0;i < arr.length;i++) {
		                                                            	if(freq[arr[i]] == 1) {
		                                                            		if(c1 == c2) {
		                                                            			ch[i] = 'A';
		                                                            			c1++;
		                                                            		}else {
		                                                            			ch[i] = 'B';
		                                                            			c2++;
		                                                            		}
		                                                            	}else {
		                                                            		if(freq[arr[i]] != 2)
		                                                            			rem = i;
		                                                            		ch[i] = 'A';
		                                                            	}
		                                                            }
		                                                            if(c1 == c2) {
		                                                            	w.println("YES");
		                                                            	for(int i = 0;i < n;i++) {
		                                                            		w.print(ch[i]);
		                                                            	}
		                                                            }else {
		                                                            	if(rem == -1) {
		                                                            		w.println("NO");
		                                                            	}else {
		                                                            		w.println("YES");
		                                                            		for(int i = 0;i < n;i++) {
		                                                            			if(i == rem) {
		                                                            				w.print('B');
		                                                            			}else {
		                                                            				w.print(ch[i]);
		                                                            			}
		                                                            		}
		                                                            	}
		                                                            }
		                                                            w.close();
		                                                     }
		                                                    
		                                                    class Pair implements Comparable<Pair>{
		                                                        long a;
		                                                        int b;
		                                                        //int c;
		                                                        Pair(long a,int b){
		                                                            this.b = b;
		                                                            this.a = a;
		                                                        }
		                                                        public boolean equals(Object o) {
		                                                            Pair p = (Pair)o;
		                                                            return this.a == p.a && this.b == p.b;
		                                                        }
		                                                        public int hashCode(){
		                                                            return Long.hashCode(a)*27 + Long.hashCode(b)* 31;
		                                                        }
		                                                        public int compareTo(Pair p) {
		                                                            return Long.compare(this.a,p.a);
		                                                        }
		                                                    }
		                                    }