Anticube

AtCoder

IDagc003_d

Time5000ms

Memory256MB

Difficulty—

Snuke got positive integers $s_1,...,s_N$ from his mother, as a birthday present. There may be duplicate elements. He will circle some of these $N$ integers. Since he dislikes cubic numbers, he wants to ensure that if both $s_i$ and $s_j (i ≠ j)$ are circled, the product $s_is_j$ is _not_ cubic. For example, when $s_1=1,s_2=1,s_3=2,s_4=4$, it is not possible to circle both $s_1$ and $s_2$ at the same time. It is not possible to circle both $s_3$ and $s_4$ at the same time, either. Find the maximum number of integers that Snuke can circle. ## Constraints * $1 ≦ N ≦ 10^5$ * $1 ≦ s_i ≦ 10^{10}$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $s_1$ : $s_N$ [samples]

Samples

Input #1

Output #1

6

Snuke can circle $1,2,3,5,6,7$.

Input #2

Output #2

Input #3

10
1
10
100
1000000007
10000000000
1000000009
999999999
999
999
999

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Anticube",
    "description": {
      "content": "Snuke got positive integers $s_1,...,s_N$ from his mother, as a birthday present. There may be duplicate elements. He will circle some of these $N$ integers. Since he dislikes cubic numbers, he wants ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 5000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc003_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Snuke got positive integers $s_1,...,s_N$ from his mother, as a birthday present. There may be duplicate elements.\nHe will circle some of these $N$ integers. Since he dislikes cubic numbers, he wants ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments