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.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.util.List;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.Collections;
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);
        OutputWriter out = new OutputWriter(outputStream);
        CVasyaAndMultisets solver = new CVasyaAndMultisets();
        solver.solve(1, in, out);
        out.close();
    }

    static class CVasyaAndMultisets {
        public void solve(int testNumber, InputReader sc, OutputWriter out) {
            int n = sc.nextInt();
            int ar[] = new int[n];
            HashMap<Integer, Integer> map = new HashMap<>();
            for (int i = 0; i < n; i++) {
                ar[i] = sc.nextInt();
                if (!map.containsKey(ar[i]))
                    map.put(ar[i], 1);
                else
                    map.put(ar[i], map.get(ar[i]) + 1);
            }
            int ones = 0;
            int two = 0;
            List<Integer> one = new ArrayList<>();
            for (int i : map.keySet()) {
                if (map.get(i) == 1) {
                    one.add(i);
                    ones++;
                }
                if (map.get(i) == 2)
                    two++;
            }
            Collections.sort(one);
            StringBuilder sb = new StringBuilder();
            if (ones % 2 == 0) {
                int done = 0;
                for (int i : ar) {
                    int a = Collections.binarySearch(one, i);
                    if (a < 0)
                        sb.append("A");
                    else if (a >= 0 && done < ones / 2) {
                        sb.append('A');
                        done++;
                    } else
                        sb.append("B");
                }
                out.println("YES");
                out.println(sb.toString());
            } else if (ones % 2 == 1 && ones + two * 2 == n) {
                out.println("NO");
            } else if (ones % 2 == 1) {
                int f = 0;
                int done = 0;
                for (int i = 0; i < n; i++) {
                    int a = Collections.binarySearch(one, ar[i]);
                    if (a < 0 && f == 0 && map.get(ar[i]) != 2) {
                        sb.append("B");
                        f++;
                    } else if (a < 0) {
                        sb.append("A");
                    } else if (done < ones / 2 + 1) {
                        sb.append("A");
                        done++;
                    } else
                        sb.append("B");
                }
                out.println("YES");
                out.println(sb.toString());
            } else {
                int j = map.size() - two;
                if (j % 2 == 1)
                    out.println("NO");
                else {
                    out.println("YES");
                    int arr[] = new int[100 + 1];
                    char ch[] = new char[101];
                    int k = 0;
                    for (int i = 0; i < n; i++) {
                        int val = ar[i];
                        if (arr[val] == 0 && k % 2 == 0) {
                            sb.append("A");
                            arr[val] = 1;
                            ch[val] = 'A';
                            k++;
                        } else if (arr[val] == 0) {
                            sb.append("B");
                            arr[val] = 1;
                            ch[val] = 'B';
                            k++;
                        } else {
                            if (ch[val] == 'A')
                                sb.append("B");
                            else
                                sb.append("A");
                        }
                    }
                    out.println(sb.toString());
                }
            }

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void println(Object... objects) {
            print(objects);
            writer.println();
        }

        public void close() {
            writer.close();
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

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

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}