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() {
  long long n, i, no = 0;
  long long *a;
  map<int, int> m;
  set<int> nice, notnice;
  cin >> n;
  a = new long long[n];
  for (i = 0; i < n; i++) {
    cin >> a[i];
    m[a[i]]++;
  }
  map<int, int>::iterator itr;
  for (itr = m.begin(); itr != m.end(); itr++) {
    if (itr->second == 1) {
      no++;
      nice.insert(itr->first);
    } else
      notnice.insert(itr->first);
  }
  if (no == 0) {
    cout << "YES" << endl;
    for (i = 0; i < n; i++) cout << "A";
    cout << endl;
  } else if (no % 2 == 0) {
    cout << "YES" << endl;
    char c = 'A';
    for (i = 0; i < n; i++) {
      if (m[a[i]] != 1)
        cout << 'A';
      else {
        cout << c;
        c = (c == 'A') ? 'B' : 'A';
      }
    }
    cout << endl;
  } else {
    char c = 'A';
    long long nA = 0, nB = 0;
    map<int, char> mapping;
    set<int>::iterator itr;
    for (itr = nice.begin(); itr != nice.end(); itr++) {
      mapping[*itr] = c;
      if (c == 'A')
        nA++;
      else
        nB++;
      c = (c == 'A') ? 'B' : 'A';
    }
    for (itr = notnice.begin(); itr != notnice.end(); itr++) {
      if (m[*itr] > 2) {
        if (nB > nA) {
          mapping[*itr] = 'A';
          nA++;
        } else if (nA > nB) {
          mapping[*itr] = 'B';
          nB++;
        } else {
          mapping[*itr] = 'A';
          m[*itr] = 2;
        }
      } else {
        mapping[*itr] = 'A';
      }
    }
    if (nA == nB) {
      cout << "YES" << endl;
      for (i = 0; i < n; i++) {
        if (m[a[i]] == 1)
          cout << mapping[a[i]];
        else {
          cout << mapping[a[i]];
          if (m[a[i]] > 2) {
            mapping[a[i]] = (mapping[a[i]] == 'A') ? 'B' : 'A';
            m[a[i]] = 2;
          }
        }
      }
    } else
      cout << "NO" << endl;
  }
  return 0;
}