Picking Up

AtCoder

IDdiverta2019_2_b

Time2000ms

Memory256MB

Difficulty—

There are $N$ balls in a two-dimensional plane. The $i$\-th ball is at coordinates $(x_i, y_i)$. We will collect all of these balls, by choosing two integers $p$ and $q$ such that $p \neq 0$ or $q \neq 0$ and then repeating the following operation: * Choose a ball remaining in the plane and collect it. Let $(a, b)$ be the coordinates of this ball. If we collected a ball at coordinates $(a - p, b - q)$ in the previous operation, the cost of this operation is $0$. Otherwise, including when this is the first time to do this operation, the cost of this operation is $1$. Find the minimum total cost required to collect all the balls when we optimally choose $p$ and $q$. ## Constraints * $1 \leq N \leq 50$ * $|x_i|, |y_i| \leq 10^9$ * If $i \neq j$, $x_i \neq x_j$ or $y_i \neq y_j$. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $x_1$ $y_1$ $:$ $x_N$ $y_N$ [samples]

Samples

Input #1

2
1 1
2 2

Output #1

1

If we choose $p = 1, q = 1$, we can collect all the balls at a cost of $1$ by collecting them in the order $(1, 1)$, $(2, 2)$.

Input #2

Output #2

1

If we choose $p = -3, q = -2$, we can collect all the balls at a cost of $1$ by collecting them in the order $(7, 8)$, $(4, 6)$, $(1, 4)$.

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Picking Up",
    "description": {
      "content": "There are $N$ balls in a two-dimensional plane. The $i$\\-th ball is at coordinates $(x_i, y_i)$. We will collect all of these balls, by choosing two integers $p$ and $q$ such that $p \\neq 0$ or $q \\ne",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "diverta2019_2_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ balls in a two-dimensional plane. The $i$\\-th ball is at coordinates $(x_i, y_i)$.\nWe will collect all of these balls, by choosing two integers $p$ and $q$ such that $p \\neq 0$ or $q \\ne...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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