∙ (Bullet)

AtCoder

IDabc168_e

Time2000ms

Memory256MB

Difficulty—

We have caught $N$ sardines. The _deliciousness_ and _fragrantness_ of the $i$\-th sardine is $A_i$ and $B_i$, respectively. We will choose one or more of these sardines and put them into a cooler. However, two sardines on bad terms cannot be chosen at the same time. The $i$\-th and $j$\-th sardines $(i \neq j)$ are on bad terms if and only if $A_i \cdot A_j + B_i \cdot B_j = 0$. In how many ways can we choose the set of sardines to put into the cooler? Since the count can be enormous, print it modulo $1000000007$. ## Constraints * All values in input are integers. * $1 \leq N \leq 2 \times 10^5$ * $-10^{18} \leq A_i, B_i \leq 10^{18}$ ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $B_1$ $:$ $A_N$ $B_N$ [samples]

Samples

Input #1

Output #1

5

There are five ways to choose the set of sardines, as follows:

*   The $1$\-st
*   The $1$\-st and $2$\-nd
*   The $2$\-nd
*   The $2$\-nd and $3$\-rd
*   The $3$\-rd

Input #2

Output #2

API Response (JSON)

{
  "problem": {
    "name": "∙ (Bullet)",
    "description": {
      "content": "We have caught $N$ sardines. The _deliciousness_ and _fragrantness_ of the $i$\\-th sardine is $A_i$ and $B_i$, respectively. We will choose one or more of these sardines and put them into a cooler. Ho",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc168_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have caught $N$ sardines. The _deliciousness_ and _fragrantness_ of the $i$\\-th sardine is $A_i$ and $B_i$, respectively.\nWe will choose one or more of these sardines and put them into a cooler. Ho...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments