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:
//package com.company;

import java.io.*;
import java.math.BigInteger;
import java.util.*;

public class Main {
    static long TIME_START, TIME_END;

    public static class Task {

        public void solve(Scanner sc, PrintWriter pw) throws IOException {
            int n = sc.nextInt();
            int[] count = new int[101];
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                int a = sc.nextInt();
                arr[i] = a;
                count[a]++;
            }
            int single = 0;
            int doub = 0;
            int multi = 0;
            for (int i = 0; i < 101; i++) {
                if (count[i] == 1) {
                    single++;
                } else if (count[i] == 2) {
                    doub++;
                } else if (count[i] > 2){
                    multi++;
                }
            }
            if (multi == 0 && single % 2 != 0) {
                pw.println("NO");
                return;
            }
            pw.println("YES");
            boolean shiftMulti = single % 2 != 0;
            StringBuilder sb = new StringBuilder();
            char giveTo = 'A';
            for (int i = 0; i < n; i++) {
                if (count[arr[i]] == 1) {
                    sb.append(giveTo);
                    giveTo = giveTo == 'A' ? 'B' : 'A';
                } else if (count[arr[i]] == 2) {
                    sb.append('A');
                } else if (count[arr[i]] > 2) {
                    if (shiftMulti) {
                        shiftMulti = false;
                        sb.append('B');
                    } else {
                        sb.append('A');
                    }
                }
            }
            pw.println(sb.toString());
        }



    }

    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
//        Scanner sc = new Scanner(new FileInputStream("Test.in"));
        PrintWriter pw = new PrintWriter(System.out);
//        PrintWriter pw = new PrintWriter(new FileOutputStream("Test.in"));
//        PrintWriter pw = new PrintWriter(new FileOutputStream("Test.out"));


        Runtime runtime = Runtime.getRuntime();
        long usedMemoryBefore = runtime.totalMemory() - runtime.freeMemory();
        TIME_START = System.currentTimeMillis();
        Task t = new Task();
        t.solve(sc, pw);
        TIME_END = System.currentTimeMillis();
        long usedMemoryAfter = runtime.totalMemory() - runtime.freeMemory();
        pw.close();
//        System.out.println("Memory increased:" + (usedMemoryAfter - usedMemoryBefore) / 1000000);
//        System.out.println("Time used: " + (TIME_END - TIME_START) + ".");
    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public Scanner(FileReader s) throws FileNotFoundException {
            br = new BufferedReader(s);
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

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

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

        public String nextLine() throws IOException {
            return br.readLine();
        }

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

        public boolean ready() throws IOException {
            return br.ready();
        }
    }
}