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;
  cin >> n;
  int a[n];
  map<int, int> mp;
  vector<int> un;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    if (mp[a[i]] == 0) {
      un.push_back(a[i]);
    }
    mp[a[i]]++;
  }
  int cnt1 = 0, cnt2 = 0, cnt3 = 0;
  for (int i = 0; i < un.size(); i++) {
    if (mp[un[i]] == 1)
      cnt1++;
    else if (mp[un[i]] == 2)
      cnt2++;
    else
      cnt3++;
  }
  if (cnt1 % 2 == 0) {
    cout << "YES" << endl;
    map<int, char> op;
    bool flg = true;
    for (int i = 0; i < un.size(); i++) {
      if (mp[un[i]] == 1) {
        if (flg) {
          op[un[i]] = 'A';
          flg = false;
        } else {
          op[un[i]] = 'B';
          flg = true;
        }
      } else
        op[un[i]] = 'A';
    }
    for (int i = 0; i < n; i++) cout << op[a[i]];
    cout << endl;
  } else {
    if (cnt3 > 0) {
      cout << "YES" << endl;
      map<int, char> op;
      bool flg = true;
      for (int i = 0; i < un.size(); i++) {
        if (mp[un[i]] == 1) {
          if (flg) {
            op[un[i]] = 'A';
            flg = false;
          } else {
            op[un[i]] = 'B';
            flg = true;
          }
        } else
          op[un[i]] = 'A';
      }
      bool fl = true;
      for (int i = 0; i < n; i++) {
        if (mp[a[i]] == 1)
          cout << op[a[i]];
        else {
          if (fl == true && mp[a[i]] != 2) {
            cout << 'B';
            fl = false;
          } else
            cout << op[a[i]];
        }
      }
      cout << endl;
    } else
      cout << "NO" << endl;
  }
}