Max Mod Min

AtCoder

IDarc147_a

Time2000ms

Memory256MB

Difficulty—

You are given a sequence of $N$ positive integers: $A=(A_1,A_2,\dots,A_N)$. You will repeat the following operation until the length of $A$ becomes $1$. * Let $k$ be the length of $A$ before this operation. Choose integers $i$ and $j$ such that $\max({A_1,A_2,\dots,A_{k}})=A_i,\min({A_1,A_2,\dots,A_{k}})=A_j$, and $i \neq j$. Then, replace $A_i$ with $(A_i \bmod A_j)$. If $A_i$ becomes $0$ at this moment, delete $A_i$ from $A$. Find the number of operations that you will perform. We can prove that, no matter how you choose $i,j$ in the operations, the total number of operations does not change. ## Constraints * $2 \le N \le 2 \times 10^5$ * $1 \le A_i \le 10^9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\dots$ $A_N$ [samples]

Samples

Input #1

3
2 3 6

Output #1

3

You will perform $3$ operations as follows:

*   Choose $i=3,j=1$. You get $A_3=0$, and delete $A_3$ from $A$. Now you have $A=(2,3)$.
*   Choose $i=2,j=1$. You get $A_2=1$. Now you have $A=(2,1)$.
*   Choose $i=1,j=2$. You get $A_1=0$, and delete $A_1$ from $A$. Now you have $A=(1)$, and terminate the process because the length of $A$ becomes $1$.

Input #2

6
1232 452 23491 34099 57341 21488

Output #2

API Response (JSON)

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  "problem": {
    "name": "Max Mod Min",
    "description": {
      "content": "You are given a sequence of $N$ positive integers: $A=(A_1,A_2,\\dots,A_N)$. You will repeat the following operation until the length of $A$ becomes $1$. *   Let $k$ be the length of $A$ before this o",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc147_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a sequence of $N$ positive integers: $A=(A_1,A_2,\\dots,A_N)$.\nYou will repeat the following operation until the length of $A$ becomes $1$.\n\n*   Let $k$ be the length of $A$ before this o...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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