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:
//package ;
import java.io.*;
import java.util.*;

public class C {
	static int c[];
	static boolean dp(int x, int a, int b) {
		if(x==101) return a==b;
		boolean ans = true;
		if(c[x]==0 || c[x] ==2)
			ans&=dp(x+1,a,b);
		else
			ans&=(dp(x+1,a+1,b)|dp(x+1,a,b+1));
		return ans;
	}
	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner();
		PrintWriter pw = new PrintWriter(System.out);
		int n =sc.nextInt();
		c=new int[101];
		int a[]=sc.nextIntArray(n);
		HashMap<Integer, ArrayList<Integer>>hm=new HashMap<>();
		for(int i=0;i<n;i++) 
		{
			c[a[i]]++;
			ArrayList<Integer> tmp = hm.getOrDefault(a[i], new ArrayList<Integer>());
			tmp.add(i);
			hm.put(a[i],tmp);
		}
		int ones = 0, more=0;
		for(int i=0;i<101;i++) {
			if(c[i]==0 ||c[i]==2)
				continue;
			if(c[i]==1) ones++;
			else more++;
		}
		if(ones%2==0) {
			pw.println("YES");
			boolean aorb=true;
			char[]ans=new char[n];
			for(int i=0;i<101;i++) {
				if(c[i]==0) continue;
				if(c[i]==1) {
					ArrayList<Integer> tmp = hm.get(i);
					ans[tmp.get(0)] = aorb?'A':'B';
					aorb = !aorb;
				}
				else {
					ArrayList<Integer> tmp = hm.get(i);
					boolean f=true;
					for(int index:tmp) {
						ans[index] = (f||tmp.size()==3)?'A':'B';
						f = !f;
					}
				}
			}
			for(char c:ans)
				pw.print(c);
		}
		else if(more>0) {
			pw.println("YES");
			boolean aorb=true;
			boolean found = false;
			char[]ans=new char[n];
			for(int i=0;i<101;i++) {
				if(c[i]==0) continue;
				if(c[i]==1) {
					ArrayList<Integer> tmp = hm.get(i);
					ans[tmp.get(0)] = aorb?'A':'B';
					aorb = !aorb;
				}
				else {
					ArrayList<Integer> tmp = hm.get(i);
					boolean f=true;
					if(!found && tmp.size()>2) {
						for(int index:tmp) {
							ans[index] = f?'B':'A';
							f = false;
						}
						found = true;
					}
					else
						for(int index:tmp) {
							ans[index] = (f||tmp.size()==3)?'A':'B';
							f = !f;
						}
				}
			}
			for(char c:ans)
				pw.print(c);
		}
		else pw.print("NO");
//		pw.println(dp(1,0,0));
		pw.close();
	}

	static class Scanner {
		BufferedReader br;
		StringTokenizer st;

		Scanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

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

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

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

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

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

		boolean hasnext() throws IOException {
			return br.ready();
		}

		public int[] nextIntArray(int n) throws IOException {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		public Integer[] nextIntegerArray(int n) throws IOException {
			Integer[] a = new Integer[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		char[] nextCharArray() throws IOException {
			return br.readLine().toCharArray();
		}

		public double[] nextDoubleArray(int n) throws IOException {
			double[] ans = new double[n];
			for (int i = 0; i < n; i++)
				ans[i] = nextDouble();
			return ans;
		}

	}
}