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.*;

public class VasyaMultisets {
    public static void main(String[] args) {
        FastScanner scanner = new FastScanner();
        PrintWriter out = new PrintWriter(System.out);
        int N = scanner.nextInt();
        int[] set = new int[N];
        int cnt[] = new int[101];
        for(int i = 0; i < N; i++) {
            set[i] = scanner.nextInt();
            cnt[set[i]]++;
        }
        int[] counters = new int[101];
        for(int i = 1; i <= 100; i++) {
            counters[cnt[i]]++;
        }
        int check = 0;
        for(int i = 3; i <= 100; i++) {
            check += counters[i];
        }
        if (check > 0 || counters[1]%2==0) {
            boolean need = counters[1]%2==1;
            char[] outArr = new char[N];
            out.println("YES");
            int target = (counters[1]+1)/2;
            for(int i = 0; i < N; i++) {
                if (cnt[set[i]] == 1 && ((target > 0 && !need) || (target > 1))) {
                    outArr[i] = 'A';
                    target--;
                }
                else if (cnt[set[i]] == 1) outArr[i] = 'B';
                else if (cnt[set[i]] > 2 && need) {
                    outArr[i] = 'A';
                    need = false;
                    target--;
                }
                else outArr[i] = 'B';

            }
            out.println(outArr);
        }
        else out.println("NO");
        out.flush();
    }

    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(Reader in) {
            br = new BufferedReader(in);
        }

        public FastScanner() {
            this(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 readNextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        int[] readIntArray(int n) {
            int[] a = new int[n];
            for (int idx = 0; idx < n; idx++) {
                a[idx] = nextInt();
            }
            return a;
        }
    }
}