Background

A standard deck of playing cards has $54$ cards. After removing the two Jokers, there are $52$ cards. In the same deck, each card can appear at most once.

A deck has four suits: spades ($\texttt{spade}$), hearts ($\texttt{heart}$), clubs ($\texttt{club}$), and diamonds ($\texttt{diamond}$). Each suit has $13$ ranks, from $\texttt{A}$ to $\texttt{K}$.

In this problem, the four suits are written as $\texttt{S,H,C,D}$.

We define that any card is written as suit + rank, and we use $\texttt{T}$ to represent $\texttt{10}$, for example $\texttt{SA,D5,HT,CQ}$.

Problem Description

Xinxin has two decks without Jokers. She will take out $n$ cards from these cards.

Xinxin created a combination called "Xiao Xinxin". It is defined as follows: take any $3$ cards. If these $3$ cards have the same rank, and the suits contain exactly two different suits, then this is called one "Xiao Xinxin" set. For example, $\texttt{H3,S3,S3}$ is one "Xiao Xinxin" set.

After three cards form a "Xiao Xinxin", Xinxin will remove them from the pile, and they cannot be used again.

Now Xinxin wants you to help her count: what is the maximum number of "Xiao Xinxin" sets that can be formed from these cards.

Input Format

The first line contains a positive integer $n$.

Lines $2$ to $n+1$ each contain one playing card.

Output Format

Output the maximum number of "Xiao Xinxin" sets that can be formed from these $n$ cards.

3
S3
H3
S3

1

7
ST
ST
HT
HT
CT
CT
DT

2

6
DA
HA
D4
C5
DA
D4

1

Hint

This problem uses bundled testdata.

• $\texttt{Subtask 1 (10 pts)}$: $1 \le n \le 3$.
• $\texttt{Subtask 2 (20 pts)}$: $1 \le n \le 5$.
• $\texttt{Subtask 3 (30 pts)}$: $1 \le n \le 20$.
• $\texttt{Subtask 4 (10 pts)}$: $1 \le n \le 70$.
• $\texttt{Subtask 5 (30 pts)}$: no special constraints.

For $100\%$ of the data, $1 \le n \le 104$, and it is guaranteed that all input cards exist in two decks without Jokers.

Translated by ChatGPT 5