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

public class CF1042_F {
    public static void main(String[] args) throws Throwable {
        MyScanner sc = new MyScanner();
        PrintWriter pw = new PrintWriter(System.out);

        int n = sc.nextInt();
        int[] a = new int[n];
        int[] c = new int[101];
        boolean[] A = new boolean[101];
        for (int i = 0; i < n; i++) {
            a[i] = sc.nextInt();
            c[a[i]]++;
        }
        int cntSingle = 0;
        ArrayList<Integer> single = new ArrayList<>();
        int other = -1;
        for (int i = 1; i <= 100; i++) {
            if (c[i] == 1) {
                cntSingle++;
                single.add(i);
            } else if (c[i] > 2)
                other = i;
        }
        for (int i = 0; i < cntSingle / 2; i++)
            A[single.get(i)] = true;
        boolean ok = true;
        if (cntSingle % 2 == 1) {
            if (other == -1)
                ok = false;
            else
                A[other] = true;
        }
        if (!ok)
            pw.println("NO");
        else {
            pw.println("YES");
            StringBuilder ans = new StringBuilder();
            for (int i = 0; i < n; i++) {
                if (A[a[i]])
                    ans.append('A');
                else
                    ans.append('B');
                if (a[i] == other && A[other] == true)
                    A[other] = false;
            }
            pw.println(ans);
        }

        pw.flush();
        pw.close();
    }

    static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            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;
        }
    }
}