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.*;
import java.util.*;
 
 
public class Main{

	public static Reader sc = new Reader();
	//public static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

   public static void main(String[] args) throws IOException{
	
	int n = sc.nextInt();
	int[] a = new int[n];
	int[] v = new int[101];
	for (int i = 0; i < n; i++) {
		a[i] = sc.nextInt();
		v[a[i]]++;
	}
	int nice = 0;
	int notnice = 0;
	for (int i = 0; i < 101; i+=1) {
		if (v[i] == 1) nice++;
		else if (v[i] >= 3) notnice++;
	}
	if (nice % 2 == 0) {
		int turn = 0;
		out.println("YES");
		for (int i = 0; i < n; i++) {
			if (v[a[i]] == 1) {
				out.print((char)('A' + turn)); 
				turn = 1-turn;
			}
			else out.print('A');
		}
		out.println();
	}
	else {
		if (notnice > 0) {
			out.println("YES");
			char[] label = new char[n];
			Arrays.fill(label, 'a');
			int turn = 0;
			int badone = 0;
			int bi = -1;
			for (int i = 0; i < n; i++) {
				if (v[a[i]] == 1) {
					label[i]=(char)('A' + turn); 
					turn = 1-turn;
				}
				if (v[a[i]] >= 3 && bi == -1) {
					badone = a[i];
					bi = i;
				}
			}
			label[bi] = (char)('A' + turn);
			turn = 1-turn;
			for (int i = 0; i < n; i++) {
				if (i == bi) continue;
				if (v[a[i]] >= 2) {
					if (a[i] == badone && i != bi) {
						label[i] = (char)('A' + turn);
					}
					else label[i] = 'A';
				}
			}
			for (char x: label) out.print(x);
			out.println();
		}
		else {
			out.println("NO");
		}
	}
	
	out.close();
   }
   static long ceil(long a, long b) {
		return (a+b-1)/b;
	}
  
   static long powMod(long base, long exp, long mod) {
	   if (base == 0 || base == 1) return base;
	   if (exp == 0) return 1;
	   if (exp == 1) return base % mod;
	   long R = powMod(base, exp/2, mod) % mod;
	   R *= R;
	   R %= mod;
	   if ((exp & 1) == 1) {
		   return base * R % mod;
	   }
	   else return R % mod;
   }
   
   static long pow(long base, long exp) {
	   if (base == 0 || base == 1) return base;
	   if (exp == 0) return 1;
	   if (exp == 1) return base;
	   long R = pow(base, exp/2);
	   if ((exp & 1) == 1) {
		   return R * R * base;
	   }
	   else return R * R;
   }
   

 
   static class Reader 
   { 
       final private int BUFFER_SIZE = 1 << 16; 
       private DataInputStream din; 
       private byte[] buffer; 
       private int bufferPointer, bytesRead; 

       public Reader() 
       { 
           din = new DataInputStream(System.in); 
           buffer = new byte[BUFFER_SIZE]; 
           bufferPointer = bytesRead = 0; 
       } 

       public Reader(String file_name) throws IOException 
       { 
           din = new DataInputStream(new FileInputStream(file_name)); 
           buffer = new byte[BUFFER_SIZE]; 
           bufferPointer = bytesRead = 0; 
       } 

       public String readLine() throws IOException 
       { 
           byte[] buf = new byte[64]; // line length 
           int cnt = 0, c;
           while ((c = read()) != -1) 
           { 
               if (c == '\n') 
               {
            	   break;
               }
               buf[cnt++] = (byte) c; 
           } 
           return new String(buf, 0, Integer.max(cnt-1, 0)); 
       } 

       public int nextInt() throws IOException 
       { 
           int ret = 0; 
           byte c = read(); 
           while (c <= ' ') 
               c = read(); 
           boolean neg = (c == '-'); 
           if (neg) 
               c = read(); 
           do
           { 
               ret = ret * 10 + c - '0'; 
           }  while ((c = read()) >= '0' && c <= '9'); 

           if (neg) 
               return -ret; 
           return ret; 
       } 

       public long nextLong() throws IOException 
       { 
           long ret = 0; 
           byte c = read(); 
           while (c <= ' ') 
               c = read(); 
           boolean neg = (c == '-'); 
           if (neg) 
               c = read(); 
           do { 
               ret = ret * 10 + c - '0'; 
           } 
           while ((c = read()) >= '0' && c <= '9'); 
           if (neg) 
               return -ret; 
           return ret; 
       } 

       public double nextDouble() throws IOException 
       { 
           double ret = 0, div = 1; 
           byte c = read(); 
           while (c <= ' ') 
               c = read(); 
           boolean neg = (c == '-'); 
           if (neg) 
               c = read(); 

           do { 
               ret = ret * 10 + c - '0'; 
           } 
           while ((c = read()) >= '0' && c <= '9'); 

           if (c == '.') 
           { 
               while ((c = read()) >= '0' && c <= '9') 
               { 
                   ret += (c - '0') / (div *= 10); 
               } 
           } 

           if (neg) 
               return -ret; 
           return ret; 
       } 

       private void fillBuffer() throws IOException 
       { 
           bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
           if (bytesRead == -1) 
               buffer[0] = -1; 
       } 

       private byte read() throws IOException 
       { 
           if (bufferPointer == bytesRead) 
               fillBuffer(); 
           return buffer[bufferPointer++]; 
       } 

       public void close() throws IOException 
       { 
           if (din == null) 
               return; 
           din.close(); 
       } 
   }

	public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
}