GCD Permutation

AtCoder

IDabc230_g

Time5000ms

Memory256MB

Difficulty—

Given is a permutation $P=(P_1,P_2,\ldots,P_N)$ of the integers from $1$ through $N$. Find the number of pairs of integers $(i,j)$ such that $1\leq i\leq j\leq N$ satisfying $GCD(i,j)\neq 1$ and $GCD(P_i,P_j)\neq 1$. Here, for positive integers $x$ and $y$, $GCD(x,y)$ denotes the greatest common divisor of $x$ and $y$. ## Constraints * $1 \leq N \leq 2\times 10^5$ * $(P_1,P_2,\ldots,P_N)$ is a permutation of $(1,2,\ldots,N)$. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $P_1$ $P_2$ $\ldots$ $P_N$ [samples]

Samples

Input #1

6
5 1 3 2 4 6

Output #1

6

Six pairs $(3,3)$, $(3,6)$, $(4,4)$, $(4,6)$, $(5,5)$, $(6,6)$ satisfy the condition, so $6$ should be printed.

Input #2

12
1 2 3 4 5 6 7 8 9 10 11 12

Output #2

API Response (JSON)

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    "name": "GCD Permutation",
    "description": {
      "content": "Given is a permutation $P=(P_1,P_2,\\ldots,P_N)$ of the integers from $1$ through $N$. Find the number of pairs of integers $(i,j)$ such that $1\\leq i\\leq j\\leq N$ satisfying $GCD(i,j)\\neq 1$ and $GCD(",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 5000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc230_g"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given is a permutation $P=(P_1,P_2,\\ldots,P_N)$ of the integers from $1$ through $N$.\nFind the number of pairs of integers $(i,j)$ such that $1\\leq i\\leq j\\leq N$ satisfying $GCD(i,j)\\neq 1$ and $GCD(...",
      "is_translate": false,
      "language": "English"
    }
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}

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