Integer Product

AtCoder

IDagc047_a

Time2000ms

Memory256MB

Difficulty—

You are given $N$ real values $A_1, A_2, \ldots, A_N$. Compute the number of pairs of indices $(i, j)$ such that $i < j$ and the product $A_i \cdot A_j$ is integer. ## Constraints * $2 \leq N \leq 200\,000$ * $0 < A_i < 10^4$ * $A_i$ is given with at most 9 digits after the decimal. ## Input Input is given from Standard Input in the following format. $N$ $A_1$ $A_2$ $\vdots$ $A_N$ [samples]

Samples

Input #1

5
7.5
2.4
17.000000001
17
16.000000000

Output #1

3

There are 3 pairs with integer product:

*   $7.5 \cdot 2.4 = 18$
*   $7.5 \cdot 16 = 120$
*   $17 \cdot 16 = 272$

Input #2

11
0.9
1
1
1.25
2.30000
5
70
0.000000001
9999.999999999
0.999999999
1.000000001

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Integer Product",
    "description": {
      "content": "You are given $N$ real values $A_1, A_2, \\ldots, A_N$. Compute the number of pairs of indices $(i, j)$ such that $i < j$ and the product $A_i \\cdot A_j$ is integer.",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc047_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given $N$ real values $A_1, A_2, \\ldots, A_N$. Compute the number of pairs of indices $(i, j)$ such that $i < j$ and the product $A_i \\cdot A_j$ is integer.\n\n## Constraints\n\n*   $2 \\leq N \\leq...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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