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 static java.lang.Double.parseDouble;
import static java.lang.Integer.MAX_VALUE;
import static java.lang.Integer.max;
import static java.lang.Long.max;
import static java.lang.Integer.parseInt;
import static java.lang.Long.parseLong;
import static java.lang.Math.abs;
import static java.lang.Math.min;
import static java.lang.Math.toRadians;
import static java.lang.System.exit;

import java.io.*;
import java.util.*;
import java.util.concurrent.atomic.AtomicBoolean;

public class A {

    static BufferedReader in;
    static PrintWriter out;
    static StringTokenizer tok;

    void solve() throws Exception {
        int n = nextInt(), x = 0;
        int a[] = new int[n], cnt1[] = new int[101], cnt2[] = new int[101];
        for (int i = 0; i < n; i++) a[i] = nextInt();
        for (int i = 0; i < n; i++) cnt1[a[i]]++;
        for (int i = 1; i <= 100; i++) if(cnt1[i] != 0) cnt2[ cnt1[i] ]++;
        for (int i = 3; i <= 100; i++) {
            if(cnt2[i]!= 0) x = i;
        }
        int k = cnt2[1] / 2;
        if(cnt2[1] % 2 == 0) {
            out.println("YES");
            for(int i = 0; i < n ; i++) {
                if(cnt1[ a[i] ] == 1 && k > 0) {
                    out.print('B');
                    k--;
                } else out.print('A');
            }
        } else if(x != 0) {
            out.println("YES");
            boolean stop = false;
            for(int i = 0; i < n ; i++) {
                if(cnt1[ a[i] ] == 1 && k > 0) {
                    out.print('B');
                    k--;
                } else {
                    if (cnt1[ a[i] ] == x && !stop) {
                        out.print('B');
                        stop = true;
                    } else out.print('A');
                }
            }
        } else {
            out.println("NO");
        }
    }

    public int lower_bound(long[] a, long v) {
        int low = -1, high = a.length;
        while (high - low > 1) {
            int h = high + low >>> 1;
            if (a[h] >= v) {
                high = h;
            } else {
                low = h;
            }
        }
        return high;
    }


    private long gcd(long a, long b) {
        while (b > 0) {
            long temp = b;
            b = a % b;
            a = temp;
        }
        return a;
    }

    private long lcm(long a, long b) {
        return a * (b / gcd(a, b));
    }

    int nextInt() throws IOException {
        return parseInt(next());
    }

    long nextLong() throws IOException {
        return parseLong(next());
    }

    double nextDouble() throws IOException {
        return parseDouble(next());
    }

    String next() throws IOException {
        while (tok == null || !tok.hasMoreTokens()) {
            tok = new StringTokenizer(in.readLine());
        }
        return tok.nextToken();
    }

    public static void main(String[] args) throws Exception {
        try {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(new OutputStreamWriter(System.out));
            //long lStartTime = System.currentTimeMillis();
            new A().solve();
            //long lEndTime = System.currentTimeMillis();
            //out.println("Elapsed time in seconds: " + (double)(lEndTime - lStartTime) / 1000.0);
            in.close();
            out.close();
        } catch (Throwable e) {
            e.printStackTrace();
            exit(1);
        }
    }
}