Prime Flip

AtCoder

IDarc080_d

Time2000ms

Memory256MB

Difficulty—

There are infinitely many cards, numbered $1$, $2$, $3$, $...$ Initially, Cards $x_1$, $x_2$, $...$, $x_N$ are face up, and the others are face down. Snuke can perform the following operation repeatedly: * Select a prime $p$ greater than or equal to $3$. Then, select $p$ consecutive cards and flip all of them. Snuke's objective is to have all the cards face down. Find the minimum number of operations required to achieve the objective. ## Constraints * $1 ≤ N ≤ 100$ * $1 ≤ x_1 < x_2 < ... < x_N ≤ 10^7$ ## Input Input is given from Standard Input in the following format: $N$ $x_1$ $x_2$ $...$ $x_N$ [samples]

Samples

Input #1

2
4 5

Output #1

2

Below is one way to achieve the objective in two operations:

*   Select $p = 5$ and flip Cards $1$, $2$, $3$, $4$ and $5$.
*   Select $p = 3$ and flip Cards $1$, $2$ and $3$.

Input #2

9
1 2 3 4 5 6 7 8 9

Output #2

3

Below is one way to achieve the objective in three operations:

*   Select $p = 3$ and flip Cards $1$, $2$ and $3$.
*   Select $p = 3$ and flip Cards $4$, $5$ and $6$.
*   Select $p = 3$ and flip Cards $7$, $8$ and $9$.

Input #3

2
1 10000000

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Prime Flip",
    "description": {
      "content": "There are infinitely many cards, numbered $1$, $2$, $3$, $...$ Initially, Cards $x_1$, $x_2$, $...$, $x_N$ are face up, and the others are face down. Snuke can perform the following operation repeated",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc080_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are infinitely many cards, numbered $1$, $2$, $3$, $...$ Initially, Cards $x_1$, $x_2$, $...$, $x_N$ are face up, and the others are face down.\nSnuke can perform the following operation repeated...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments