Five, Five Everywhere

AtCoder

IDabc096_d

Time2000ms

Memory256MB

Difficulty—

Print a sequence $a_1, a_2, ..., a_N$ whose length is $N$ that satisfies the following conditions: * $a_i$ $(1 \leq i \leq N)$ is a prime number at most $55$ $555$. * The values of $a_1, a_2, ..., a_N$ are all different. * In every choice of five different integers from $a_1, a_2, ..., a_N$, the sum of those integers is a composite number. If there are multiple such sequences, printing any of them is accepted. ## Constraints * $N$ is an integer between $5$ and $55$ (inclusive). ## Input Input is given from Standard Input in the following format: $N$ [samples] ## Notes An integer $N$ not less than $2$ is called a prime number if it cannot be divided evenly by any integers except $1$ and $N$, and called a composite number otherwise.

Samples

Input #1

Output #1

3 5 7 11 31

Let us see if this output actually satisfies the conditions.  
First, $3$, $5$, $7$, $11$ and $31$ are all different, and all of them are prime numbers.  
The only way to choose five among them is to choose all of them, whose sum is $a_1+a_2+a_3+a_4+a_5=57$, which is a composite number.  
There are also other possible outputs, such as `2 3 5 7 13`, `11 13 17 19 31` and `7 11 5 31 3`.

Input #2

Output #2

2 3 5 7 11 13

*   $2$, $3$, $5$, $7$, $11$, $13$ are all different prime numbers.
*   $2+3+5+7+11=28$ is a composite number.
*   $2+3+5+7+13=30$ is a composite number.
*   $2+3+5+11+13=34$ is a composite number.
*   $2+3+7+11+13=36$ is a composite number.
*   $2+5+7+11+13=38$ is a composite number.
*   $3+5+7+11+13=39$ is a composite number.

Thus, the sequence `2 3 5 7 11 13` satisfies the conditions.

Input #3

Output #3

2 5 7 13 19 37 67 79

API Response (JSON)

{
  "problem": {
    "name": "Five, Five Everywhere",
    "description": {
      "content": "Print a sequence $a_1, a_2, ..., a_N$ whose length is $N$ that satisfies the following conditions: *   $a_i$ $(1 \\leq i \\leq N)$ is a prime number at most $55$ $555$. *   The values of $a_1, a_2, ...",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc096_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Print a sequence $a_1, a_2, ..., a_N$ whose length is $N$ that satisfies the following conditions:\n\n*   $a_i$ $(1 \\leq i \\leq N)$ is a prime number at most $55$ $555$.\n*   The values of $a_1, a_2, ......",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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