Brave CHAIN

AtCoder

IDabc176_f

Time2000ms

Memory256MB

Difficulty—

We have $3N$ cards arranged in a row from left to right, where each card has an integer between $1$ and $N$ (inclusive) written on it. The integer written on the $i$\-th card from the left is $A_i$. You will do the following operation $N-1$ times: * Rearrange the five leftmost cards in any order you like, then remove the three leftmost cards. If the integers written on those three cards are all equal, you gain $1$ point. After these $N-1$ operations, if the integers written on the remaining three cards are all equal, you will gain $1$ additional point. Find the maximum number of points you can gain. ## Constraints * $1 \leq N \leq 2000$ * $1 \leq A_i \leq N$ ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\cdots$ $A_{3N}$ [samples]

Samples

Input #1

2
1 2 1 2 2 1

Output #1

2

Let us rearrange the five leftmost cards so that the integers written on the six cards will be $2\ 2\ 2\ 1\ 1\ 1$ from left to right.
Then, remove the three leftmost cards, all of which have the same integer $2$, gaining $1$ point.
Now, the integers written on the remaining cards are $1\ 1\ 1$.
Since these three cards have the same integer $1$, we gain $1$ more point.
In this way, we can gain $2$ points - which is the maximum possible.

Input #2

3
1 1 2 2 3 3 3 2 1

Output #2

Input #3

3
1 1 2 2 2 3 3 3 1

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Brave CHAIN",
    "description": {
      "content": "We have $3N$ cards arranged in a row from left to right, where each card has an integer between $1$ and $N$ (inclusive) written on it. The integer written on the $i$\\-th card from the left is $A_i$. Y",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc176_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have $3N$ cards arranged in a row from left to right, where each card has an integer between $1$ and $N$ (inclusive) written on it. The integer written on the $i$\\-th card from the left is $A_i$.\nY...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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