Non-coprime DAG

AtCoder

IDarc136_e

Time2000ms

Memory256MB

Difficulty—

We have a directed graph $G$ with $N$ vertices numbered $1$ to $N$. Between two vertices $i,j$ ($1 \leq i,j \leq N$, $i \neq j$), there is an edge $i \to j$ if and only if both of the following conditions are satisfied. * $i<j$ * $\mathrm{gcd}(i,j)>1$ Additionally, each vertex has an associated value: the value of Vertex $i$ is $A_i$. Consider choosing a set $s$ of vertices so that the following condition is satisfied. * For every pair $(x,y)$ ($x<y$) of different vertices in $s$, $y$ is unreachable from $x$ in $G$. Find the maximum possible total value of vertices in $s$. ## Constraints * $1 \leq N \leq 10^6$ * $1 \leq A_i \leq 10^9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\cdots$ $A_N$ [samples]

Samples

Input #1

6
1 1 1 1 1 1

Output #1

4

We should choose $s={1,2,3,5}$.

Input #2

6
1 2 1 3 1 6

Output #2

8

We should choose $s={1,5,6}$.

Input #3

20
40 39 31 54 27 31 80 3 62 66 15 72 21 38 74 49 15 24 44 3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Non-coprime DAG",
    "description": {
      "content": "We have a directed graph $G$ with $N$ vertices numbered $1$ to $N$. Between two vertices $i,j$ ($1 \\leq i,j \\leq N$, $i \\neq j$), there is an edge $i \\to j$ if and only if both of the following condit",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc136_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a directed graph $G$ with $N$ vertices numbered $1$ to $N$.\nBetween two vertices $i,j$ ($1 \\leq i,j \\leq N$, $i \\neq j$), there is an edge $i \\to j$ if and only if both of the following condit...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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