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.io.IOException;
import java.io.InputStreamReader;
import java.util.TreeSet;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author NMouad21
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FReader in = new FReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        CVasyaAndMultisets solver = new CVasyaAndMultisets();
        solver.solve(1, in, out);
        out.close();
    }

    static class CVasyaAndMultisets {
        private int n;
        private int[] a;
        private int[] cnt;

        public void solve(int testNumber, FReader in, PrintWriter out) {
            n = in.nextInt();
            a = new int[n];
            cnt = new int[101];
            for (int i = 0; i < n; ++i) {
                a[i] = in.nextInt();
                ++cnt[a[i]];
            }

            int fuck = 0, aboveFuck = 0;
            for (int i = 0; i < n; ++i) {
                if (cnt[a[i]] == 1) {
                    ++fuck;
                } else if (cnt[a[i]] > 2) {
                    ++aboveFuck;
                }
            }

            if (fuck % 2 == 1) {
                if (aboveFuck == 0) {
                    out.print("NO");
                } else {
                    out.println("YES");

                    TreeSet<Pair<Integer, Integer>> A = new TreeSet<>(), B = new TreeSet<>();
                    for (int i = 0, taken = 0; i < n; ++i) {
                        if (cnt[a[i]] == 0) continue;
                        if (cnt[a[i]] != 1) continue;

                        if (taken < fuck / 2) {
                            A.add(new Pair<>(a[i], i));
                            ++taken;
                        } else {
                            B.add(new Pair<>(a[i], i));
                        }

                        cnt[a[i]] = 0;
                    }

                    int taken = -1;
                    for (int i = 0; i < n; ++i) {
                        if (cnt[a[i]] == 1) continue;

                        if (taken == -1 && cnt[a[i]] > 2) {
                            A.add(new Pair<>(a[i], i));
                            taken = a[i];
                        } else if (taken == a[i]) {
                            B.add(new Pair<>(a[i], i));
                        }
                    }
                    cnt[taken] = 0;

                    for (int i = 0; i < n; ++i) {
                        if (cnt[a[i]] == 0) continue;
                        A.add(new Pair<>(a[i], i));
                    }

                    for (int i = 0; i < n; ++i) {
                        if (A.contains(new Pair<>(a[i], i))) {
                            out.print('A');
                        } else {
                            out.print('B');
                        }
                    }
                }
            } else {
                out.println("YES");
                for (int i = 0, olala = 0; i < n; ++i) {
                    if (cnt[a[i]] == 1) {
                        if ((olala << 1) < fuck) {
                            ++olala;
                            out.print('A');
                        } else {
                            out.print('B');
                        }
                    } else {
                        out.print('A');
                    }
                }
            }
        }

    }

    static class Pair<F extends Comparable<F>, S extends Comparable<S>> implements Comparable<Pair<F, S>> {
        public F f;
        public S s;

        public Pair() {
        }

        public Pair(F first, S second) {
            this.f = first;
            this.s = second;
        }

        public int compareTo(Pair<F, S> fsPair) {
            int cmp = f.compareTo(fsPair.f);
            if (cmp == 0)
                return s.compareTo(fsPair.s);
            return cmp;
        }

        public boolean equals(Object o) {
            if (o == null || o.getClass() != this.getClass())
                return false;
            return compareTo((Pair<F, S>) o) == 0;
        }

        public String toString() {
            return "First: " + f + ", Second: " + s;
        }

    }

    static class FReader {
        private BufferedReader r;
        private String line;
        private StringTokenizer st;
        private String token;

        public FReader() {
            this(System.in);
        }

        public FReader(InputStream i) {
            r = new BufferedReader(new InputStreamReader(i));
        }

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

        private String peekToken() {
            if (token == null)
                try {
                    while (st == null || !st.hasMoreTokens()) {
                        line = r.readLine();
                        if (line == null) return null;
                        st = new StringTokenizer(line);
                    }
                    token = st.nextToken();
                } catch (IOException e) {
                }
            return token;
        }

        private String nextToken() {
            String ans = peekToken();
            token = null;
            return ans;
        }

    }
}