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.InputStreamReader;
import java.util.HashMap;
import java.util.StringTokenizer;

public class CF1051C {

    public static void main(String[] args) {
        FastReader fr = new FastReader();
        int n = fr.nextInt();
        int[] arr = new int[n];
        int[] tempArr = new int[102];
        int oneCount = 0;
        int moreThanTwo = 0;
        HashMap<Integer,Integer> hm = new HashMap<Integer, Integer>();
        for(int i=0;i<n;i++) {
            arr[i] = fr.nextInt();
            tempArr[arr[i]]++;
        }
        for(int i=1;i<=100;i++) {
            if(tempArr[i]==1) {
                oneCount++;
                hm.put(i,1);
            }
            else if(tempArr[i]==2) {
                hm.put(i,4);
            }
            else if(tempArr[i]>2) {
                moreThanTwo++;
                hm.put(i,3);
            }
        }
        if(oneCount%2==0) {
            System.out.println("YES");
            StringBuilder sb = new StringBuilder();
            String alt1 = "A";
            String alt2 = "B";
            for(int i=0;i<n;i++) {
                if(hm.get(arr[i])==1) {
                    sb.append(alt1);
                    String temp = alt2;
                    alt2 = alt1;
                    alt1 = temp;
                }
                else
                {
                    sb.append("A");
                }
            }
            System.out.println(sb.toString());
        }
        else {
            if(moreThanTwo!=0) {
                System.out.println("YES");
                StringBuilder sb = new StringBuilder();
                String alt1 = "A";
                String alt2 = "B";
                boolean onlyOneDone = false;
                for(int i=0;i<n;i++) {
                    if(hm.get(arr[i])==1) {
                        sb.append(alt1);
                        String temp = alt2;
                        alt2 = alt1;
                        alt1 = temp;
                    }
                    else if(hm.get(arr[i])==3 && !onlyOneDone)
                    {
                        onlyOneDone = true;
                        sb.append("B");
                    }
                    else
                        sb.append("A");
                }
                System.out.println(sb.toString());
            }
            else
                System.out.println("NO");
        }
    }

    //Better IO Class
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        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();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public Double nextDouble() {
            return Double.parseDouble(next());
        }

        public Float nextFloat() {
            return Float.parseFloat(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                System.out.println(e);
            }
            return str;
        }
    }

}