Almost GCD

AtCoder

IDabc182_b

Time2000ms

Memory256MB

Difficulty—

Given is an integer sequence $A$: $A_1, A_2, A_3, \dots, A_N$. Let the _GCD-ness_ of a positive integer $k$ be the number of elements among $A_1, A_2, A_3, \dots, A_N$ that are divisible by $k$. Among the integers greater than or equal to $2$, find the integer with the greatest GCD-ness. If there are multiple such integers, you may print any of them. ## Constraints * $1 \le N \le 100$ * $2 \le A_i \le 1000$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A_1 \hspace{7pt} A_2 \hspace{7pt} A_3 \hspace{5pt} \dots \hspace{5pt} A_N$ [samples]

Samples

Input #1

3
3 12 7

Output #1

3

Among $3$, $12$, and $7$, two of them - $3$ and $12$ - are divisible by $3$, so the GCD-ness of $3$ is $2$.  
No integer greater than or equal to $2$ has greater GCD-ness, so $3$ is a correct answer.

Input #2

5
8 9 18 90 72

Output #2

9

In this case, the GCD-ness of $9$ is $4$.  
$2$ and $3$ also have the GCD-ness of $4$, so you may also print $2$ or $3$.

Input #3

5
1000 1000 1000 1000 1000

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Almost GCD",
    "description": {
      "content": "Given is an integer sequence $A$: $A_1, A_2, A_3, \\dots, A_N$.   Let the _GCD-ness_ of a positive integer $k$ be the number of elements among $A_1, A_2, A_3, \\dots, A_N$ that are divisible by $k$.   A",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc182_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given is an integer sequence $A$: $A_1, A_2, A_3, \\dots, A_N$.  \nLet the _GCD-ness_ of a positive integer $k$ be the number of elements among $A_1, A_2, A_3, \\dots, A_N$ that are divisible by $k$.  \nA...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments