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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
        public static void main(String[] args) {
                InputStream inputStream = System.in;
                OutputStream outputStream = System.out;
                InputReader in = new InputReader(inputStream);
                PrintWriter out = new PrintWriter(outputStream);
                TaskC solver = new TaskC();
                solver.solve(1, in, out);
                out.close();
        }

        static class TaskC {
                public void solve(int testNumber, InputReader in, PrintWriter out) {
                        int n = in.i();
                        int[] freq = new int[105];
                        int[] a = in.ia(n);
                        for (int i = 0; i < n; i++) {
                                freq[a[i]]++;
                        }
                        int count2 = 0;
                        int countMoreThan2 = 0;
                        int count1 = 0;
                        for (int i = 0; i < 105; i++) {
                                if (freq[i] == 2) count2++;
                                if (freq[i] > 2) countMoreThan2++;
                                if (freq[i] == 1) count1++;
                        }

                        if (count1 % 2 == 1 && countMoreThan2 == 0) {
                                out.println("NO");
                                return;
                        }
                        if (count1 % 2 == 1 && countMoreThan2 != 0) {
                                out.println("YES");
                                StringBuilder sb = new StringBuilder();
                                boolean Y = true;
                                boolean moreThanTwo = true;
                                boolean isA = true;
                                for (int i = 0; i < n; i++) {
                                        if (freq[a[i]] == 1) {
                                                if (Y) {
                                                        sb.append('A');
                                                } else {
                                                        sb.append('B');
                                                }
                                                Y = !Y;
                                        }
                                        if (freq[a[i]] == 2) {
                                                sb.append('A');
                                        }
                                        if (freq[a[i]] > 2 && !moreThanTwo) {
                                                if (!isA) {
                                                        sb.append('A');
                                                } else {
                                                        sb.append('B');
                                                }
                                        }
                                        if (freq[a[i]] > 2 & moreThanTwo) {
                                                moreThanTwo = false;
                                                if (Y) {
                                                        sb.append('A');
                                                } else {
                                                        sb.append('B');
                                                        isA = false;
                                                }
                                                Y = !Y;
                                        }
                                }
                                out.println(sb.toString());
                        }
                        if (count1 % 2 == 0) {
                                out.println("YES");
                                StringBuilder sb = new StringBuilder();
                                boolean Y = true;
                                for (int i = 0; i < n; i++) {
                                        if (freq[a[i]] == 1) {
                                                if (Y) {
                                                        sb.append('A');
                                                } else {
                                                        sb.append('B');
                                                }
                                                Y = !Y;
                                        } else {
                                                sb.append('A');
                                        }
                                }
                                out.println(sb.toString());
                        }
                }

        }

        static class InputReader {
                InputStream is;
                private byte[] inbuf = new byte[1024];
                public int lenbuf = 0;
                public int ptrbuf = 0;

                public InputReader(InputStream is) {
                        this.is = is;
                }

                private int readByte() {
                        if (lenbuf == -1) throw new InputMismatchException();
                        if (ptrbuf >= lenbuf) {
                                ptrbuf = 0;
                                try {
                                        lenbuf = is.read(inbuf);
                                } catch (IOException e) {
                                        throw new InputMismatchException();
                                }
                                if (lenbuf <= 0) return -1;
                        }
                        return inbuf[ptrbuf++];
                }

                public int[] ia(int n) {
                        int[] a = new int[n];
                        for (int i = 0; i < n; i++) a[i] = i();
                        return a;
                }

                public int i() {
                        int num = 0, b;
                        boolean minus = false;
                        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
                        if (b == '-') {
                                minus = true;
                                b = readByte();
                        }

                        while (true) {
                                if (b >= '0' && b <= '9') {
                                        num = num * 10 + (b - '0');
                                } else {
                                        return minus ? -num : num;
                                }
                                b = readByte();
                        }
                }

        }
}