Yet Another mod M

AtCoder

IDabc272_g

Time2000ms

Memory256MB

Difficulty—

You are given a sequence $A=(A_1,A_2,\dots,A_N)$ of length $N$ consisting of positive integers, where the elements of $A$ are distinct. You will choose a positive integer $M$ between $3$ and $10^9$ (inclusive) to perform the following operation once: * For each integer $i$ such that $1 \le i \le N$, replace $A_i$ with $A_i \bmod M$. Can you choose an $M$ so that $A$ satisfies the following condition after the operation? If you can, find such an $M$. * There exists an integer $x$ such that $x$ is the majority in $A$. Here, an integer $x$ is said to be the majority in $A$ if the number of integers $i$ such that $A_i = x$ is greater than the number of integers $i$ such that $A_i \neq x$. ## Constraints * $3 \le N \le 5000$ * $1 \le A_i \le 10^9$ * The elements of $A$ are distinct. * All values in the input are integers. ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\dots$ $A_N$ [samples]

Samples

Input #1

5
3 17 8 14 10

Output #1

7

If you let $M=7$ to perform the operation, you will have $A=(3,3,1,0,3)$, where $3$ is the majority in $A$, so $M=7$ satisfies the condition.

Input #2

10
822848257 553915718 220834133 692082894 567771297 176423255 25919724 849988238 85134228 235637759

Output #2

Input #3

10
1 2 3 4 5 6 7 8 9 10

Output #3

\-1

API Response (JSON)

{
  "problem": {
    "name": "Yet Another mod M",
    "description": {
      "content": "You are given a sequence $A=(A_1,A_2,\\dots,A_N)$ of length $N$ consisting of positive integers, where the elements of $A$ are distinct. You will choose a positive integer $M$ between $3$ and $10^9$ (i",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc272_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a sequence $A=(A_1,A_2,\\dots,A_N)$ of length $N$ consisting of positive integers, where the elements of $A$ are distinct.\nYou will choose a positive integer $M$ between $3$ and $10^9$ (i...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments