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 A {
	static FastReader sc=null;

	public static void main(String[] args) {
		sc=new FastReader();
		int n=sc.nextInt(),nax=105;
		boolean contains=false;
		boolean po=true;
		int b=-1;
		int a[]=sc.readArray(n);
		int counts[]=new int[nax];
		ArrayList<Integer> id[]=new ArrayList[nax];
		for(int i=0;i<nax;i++)id[i]=new ArrayList<>();
		for(int i=0;i<n;i++)id[a[i]].add(i);
		for(int e:a) counts[e]++;
		int c=0;
		char ans[]=new char[n];
		for(int i=0;i<nax;i++) {
			if(counts[i]>0) {
				if(counts[i]==1)c++;
				else if(counts[i]>2 && (!contains)) {
					b=i;
					contains=true;
				}
			}
		}
		if(c==0) {
			Arrays.fill(ans, 'A');
		}
		else if(c%2==0) {
			int curr=0;
			for(int i=0;i<nax;i++) {
				if(counts[i]==0)continue;
				if(counts[i]>1) {
					for(int e:id[i])ans[e]='A';
				}
				else {
					ans[id[i].get(0)]=(curr%2==0?'A':'B');
					curr++;
				}
			}
		}
		else {
			if(!contains)po=false;
			else{
				int curr=0;
				for(int i=0;i<nax;i++) {
					if(counts[i]==0)continue;
					if(counts[i]>1) {
						for(int e:id[i])ans[e]='A';
					}
					else {
						ans[id[i].get(0)]=(curr%2==0?'A':'B');
						curr++;
					}
				}
				ans[id[b].get(0)]='B';
			}
		}
		if(!po)System.out.println("NO");
		else {
			System.out.println("YES");
			System.out.println(ans);
		}
		
		
		
			
	}
	
	
 
	
	static int[] reverseSort(int a[]) {
		ArrayList<Integer> al=new ArrayList<>();
		for(int i:a)al.add(i);
		Collections.sort(al,Collections.reverseOrder());
		for(int i=0;i<a.length;i++)a[i]=al.get(i);
		return a;
	}
	static int gcd(int a,int b) {
		if(b==0)return a;
		else return gcd(b,a%b);
	}
	static long gcd(long a,long b) {
		if(b==0)return a;
		else return gcd(b,a%b);
	}
	static void reverse(int a[]) {
		int n=a.length;
		int b[]=new int[n];
		for(int i=0;i<n;i++)b[i]=a[n-1-i];
		for(int i=0;i<n;i++)a[i]=b[i];
	}
	static int[] ruffleSort(int a[]) {
		ArrayList<Integer> al=new ArrayList<>();
		for(int i:a)al.add(i);
		Collections.sort(al);
		for(int i=0;i<a.length;i++)a[i]=al.get(i);
		return a;
	}
	
	
	
	static void print(int a[]) {
		for(int e:a) {
			System.out.print(e+" ");
		}
		System.out.println();
	}
	static void print(long a[]) {
		for(long e:a) {
			System.out.print(e+" ");
		}
		System.out.println();
	}
	
	
	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; 
        } 
        int[] readArray(int n) {
    		int a[]=new int [n];
    		for(int i=0;i<n;i++) {
    			a[i]=sc.nextInt();
    		}
    		return a;
    	}
    } 
}