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 javafx.util.Pair;

import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintStream;
import java.io.PrintWriter;
import java.lang.reflect.Array;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Map;
import java.util.Objects;
import java.util.Set;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

/**
 * Created by timur on 28.03.15.
 */

public class TaskC {
    boolean eof;
    BufferedReader br;
    StringTokenizer st;
    PrintWriter out;

    public static void main(String[] args) throws IOException {
        new TaskC().run();
    }

    public String nextToken() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                eof = true;
                return "-1";
            }
        }
        return st.nextToken();
    }

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

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

    double nextDouble() {
        return Double.parseDouble(nextToken());
    }

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


    void run() throws IOException {
        InputStream input = System.in;
        PrintStream output = System.out;
        try {
            File f = new File("a.in");
            if (f.exists() && f.canRead()) {
                input = new FileInputStream(f);
                output = new PrintStream("a.out");
            }
        } catch (Throwable e) {
        }
        br = new BufferedReader(new InputStreamReader(input));
        out = new PrintWriter(output);
        solve();
        br.close();
        out.close();
    }

    void solve() {
        int n = nextInt();
        int uc = 0, oc = 0;
        int[] a = new int[n];
        int[] s = new int[101];
        for (int i = 0; i < n; i++) {
            a[i] = nextInt();
            s[a[i]]++;
        }
        for (int i = 0; i < 101; i++) {
            if (s[i] == 1) {
                uc++;
            } else  if (s[i] > 2) {
                oc++;
            }
        }

        if (uc % 2 == 1 && oc == 0) {
            out.print("NO");
        } else {
            out.println("YES");
            int fc = 0;
            if (uc % 2 == 0) {
                for (int i = 0; i < n; i++) {
                    if (s[a[i]] == 1) {
                        if (fc < uc) {
                            out.print("A");
                            fc++;
                            uc--;
                        } else {
                            out.print("B");
                        }
                    } else {
                        out.print("A");
                    }
                }
            } else {
                boolean done = false;
                for (int i = 0; i < n; i++) {
                    if (s[a[i]] == 1) {
                        if (fc < uc) {
                            out.print("A");
                            fc++;
                            uc--;
                        } else {
                            out.print("B");
                        }
                    } else if (s[a[i]] > 2) {
                        if (done) {
                            out.print("A");
                        } else {
                            out.print("B");
                            done = true;
                        }
                    } else {
                        out.print("A");
                    }
                }
            }
        }
    }
}