LCMs

AtCoder

IDagc038_c

Time2000ms

Memory256MB

Difficulty—

We have an integer sequence of length $N$: $A_0,A_1,\cdots,A_{N-1}$. Find the following sum ($\mathrm{lcm}(a, b)$ denotes the least common multiple of $a$ and $b$): * $\sum_{i=0}^{N-2} \sum_{j=i+1}^{N-1} \mathrm{lcm}(A_i,A_j)$ Since the answer may be enormous, compute it modulo $998244353$. ## Constraints * $1 \leq N \leq 200000$ * $1 \leq A_i \leq 1000000$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A_0\ A_1\ \cdots\ A_{N-1}$ [samples]

Samples

Input #1

3
2 4 6

Output #1

22

$\mathrm{lcm}(2,4)+\mathrm{lcm}(2,6)+\mathrm{lcm}(4,6)=4+6+12=22$.

Input #2

8
1 2 3 4 6 8 12 12

Output #2

Input #3

10
356822 296174 484500 710640 518322 888250 259161 609120 592348 713644

Output #3

353891724

API Response (JSON)

{
  "problem": {
    "name": "LCMs",
    "description": {
      "content": "We have an integer sequence of length $N$: $A_0,A_1,\\cdots,A_{N-1}$. Find the following sum ($\\mathrm{lcm}(a, b)$ denotes the least common multiple of $a$ and $b$): *   $\\sum_{i=0}^{N-2} \\sum_{j=i+1}",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc038_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have an integer sequence of length $N$: $A_0,A_1,\\cdots,A_{N-1}$.\nFind the following sum ($\\mathrm{lcm}(a, b)$ denotes the least common multiple of $a$ and $b$):\n\n*   $\\sum_{i=0}^{N-2} \\sum_{j=i+1}...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments