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:
// Working program with FastReader 

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.Scanner;
import java.util.StringTokenizer;

public class RelativePrime {

    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;
        }
    }

    public static void main(String[] args) {
        FastReader s = new FastReader();
        int[] map = new int[102];
        int[] arr = new int[110];
        int n = s.nextInt();
        int niceCount = 0;
        int specialIndex = -1;
        for (int i = 0; i < n; i++) {
            arr[i] = s.nextInt();
            map[arr[i]]++;
            if (map[arr[i]] == 1) {
                niceCount++;
            } else if (map[arr[i]] == 2) {
                niceCount--;
            }
            if (map[arr[i]] > 2) {
                specialIndex = i;
            }
        }

        if (niceCount % 2 != 0 && specialIndex == -1) {
            System.out.println("NO");
            return;
        }

     
        System.out.println("YES");
        String str = "";
        int tillNow = 0;
        int specialIndexCount = specialIndex != -1 ? map[arr[specialIndex]] : 0;
        int firstHalf = (niceCount % 2 != 0) ? niceCount / 2 + 1 : niceCount / 2;
        for (int i = 0; i < n; i++) {
            if (niceCount % 2 != 0) {

                if (arr[i] == arr[specialIndex] && specialIndexCount > 1) {
                    specialIndexCount--;
                    str = str + "A";
                    continue;
                } else if (arr[i] == arr[specialIndex] && specialIndexCount == 1) {
                    specialIndexCount--;
                    str = str + "B";
                    continue;
                }

            }

            if (map[arr[i]] > 1) {
                str = str + "A";
            } else if (tillNow < firstHalf) {
                str = str + "A";
                tillNow++;
            } else {
                str = str + "B";
            }

        }
        System.out.println(str);
    }
}