mod M

AtCoder

IDarc148_a

Time2000ms

Memory256MB

Difficulty—

You are given a sequence $A = (A_1, A_2, ..., A_N)$. You may perform the following operation exactly once. * Choose an integer $M$ at least $2$. Then, for every integer $i$ ($1 \leq i \leq N$), replace $A_i$ with the remainder when $A_i$ is divided by $M$. For instance, if $M = 4$ is chosen when $A = (2, 7, 4)$, $A$ becomes $(2 \bmod 4, 7 \bmod 4, 4 \bmod 4) = (2, 3, 0)$. Find the minimum possible number of different elements in $A$ after the operation. ## Constraints * $2 \leq N \leq 2 \times 10^5$ * $0 \leq A_i \leq 10^9$ * 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

3
1 4 8

Output #1

2

If you choose $M = 3$, you will have $A = (1 \bmod 3, 4 \bmod 3, 8 \bmod 3) = (1, 1, 2)$, where $A$ contains two different elements.  
The number of different elements in $A$ cannot become $1$, so the answer is $2$.

Input #2

4
5 10 15 20

Output #2

1

If you choose $M = 5$, you will have $A = (0, 0, 0, 0)$, which is optimal.

Input #3

10
3785 5176 10740 7744 3999 3143 9028 2822 4748 6888

Output #3

API Response (JSON)

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    "name": "mod M",
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      "content": "You are given a sequence $A = (A_1, A_2, ..., A_N)$.   You may perform the following operation exactly once. *   Choose an integer $M$ at least $2$. Then, for every integer $i$ ($1 \\leq i \\leq N$), r",
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    "difficulty": "None",
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    "sign": "arc148_a"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a sequence $A = (A_1, A_2, ..., A_N)$.  \nYou may perform the following operation exactly once.\n\n*   Choose an integer $M$ at least $2$. Then, for every integer $i$ ($1 \\leq i \\leq N$), r...",
      "is_translate": false,
      "language": "English"
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