GCD on Blackboard

AtCoder

IDabc125_c

Time2000ms

Memory256MB

Difficulty—

There are $N$ integers, $A_1, A_2, ..., A_N$, written on the blackboard. You will choose one of them and replace it with an integer of your choice between $1$ and $10^9$ (inclusive), possibly the same as the integer originally written. Find the maximum possible greatest common divisor of the $N$ integers on the blackboard after your move. ## Constraints * All values in input are integers. * $2 \leq N \leq 10^5$ * $1 \leq A_i \leq 10^9$ ## Output Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $...$ $A_N$ [samples] ## Output Print the maximum possible greatest common divisor of the $N$ integers on the blackboard after your move.

Samples

Input #1

3
7 6 8

Output #1

2

If we replace $7$ with $4$, the greatest common divisor of the three integers on the blackboard will be $2$, which is the maximum possible value.

Input #2

3
12 15 18

Output #2

Input #3

2
1000000000 1000000000

Output #3

1000000000

We can replace an integer with itself.

API Response (JSON)

{
  "problem": {
    "name": "GCD on Blackboard",
    "description": {
      "content": "There are $N$ integers, $A_1, A_2, ..., A_N$, written on the blackboard. You will choose one of them and replace it with an integer of your choice between $1$ and $10^9$ (inclusive), possibly the same",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc125_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ integers, $A_1, A_2, ..., A_N$, written on the blackboard.\nYou will choose one of them and replace it with an integer of your choice between $1$ and $10^9$ (inclusive), possibly the same...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments