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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  int n;
  int vis[105], v[105];
  char mp[105];
  int ans = 0, cnt = 0;
  memset(vis, 0, sizeof(vis));
  memset(mp, 0, sizeof(mp));
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    scanf("%d", &v[i]);
    vis[v[i]]++;
  }
  int tA = 0, num = 0;
  for (int i = 0; i < n; i++) {
    if (vis[v[i]] == 1) {
      ans++;
      mp[i] = 'A' + tA;
      tA = 1 ^ tA;
    }
    if (mp[i] != 'A' && mp[i] != 'B') mp[i] = 'A';
    if (vis[v[i]] >= 3) cnt++;
  }
  if (ans % 2 == 1 && cnt == 0) {
    puts("NO");
    return 0;
  }
  if (ans % 2 == 1) {
    for (int i = 0; i < n; i++) {
      if (vis[v[i]] >= 3) {
        mp[i] = 'B';
        break;
      }
    }
  }
  puts("YES");
  printf("%s\n", mp);
  return 0;
}