Mr.Aoki Incubator

AtCoder

IDagc015_e

Time2000ms

Memory256MB

Difficulty—

Takahashi is an expert of Clone Jutsu, a secret art that creates copies of his body. On a number line, there are $N$ copies of Takahashi, numbered $1$ through $N$. The $i$\-th copy is located at position $X_i$ and starts walking with velocity $V_i$ in the positive direction at time $0$. Kenus is a master of Transformation Jutsu, and not only can he change into a person other than himself, but he can also transform another person into someone else. Kenus can select some of the copies of Takahashi at time $0$, and transform them into copies of Aoki, another Ninja. The walking velocity of a copy does not change when it transforms. From then on, whenever a copy of Takahashi and a copy of Aoki are at the same coordinate, that copy of Takahashi transforms into a copy of Aoki. Among the $2^N$ ways to transform some copies of Takahashi into copies of Aoki at time $0$, in how many ways will all the copies of Takahashi become copies of Aoki after a sufficiently long time? Find the count modulo $10^9+7$. ## Constraints * $1 ≤ N ≤ 200000$ * $1 ≤ X_i,V_i ≤ 10^9(1 ≤ i ≤ N)$ * $X_i$ and $V_i$ are integers. * All $X_i$ are distinct. * All $V_i$ are distinct. ## Input The input is given from Standard Input in the following format: $N$ $X_1$ $V_1$ : $X_N$ $V_N$ [samples]

Samples

Input #1

Output #1

6

All copies of Takahashi will turn into copies of Aoki after a sufficiently long time if Kenus transforms one of the following sets of copies of Takahashi into copies of Aoki: $(2)$, $(3)$, $(1,2)$, $(1,3)$, $(2,3)$ and $(1,2,3)$.

Input #2

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Mr.Aoki Incubator",
    "description": {
      "content": "Takahashi is an expert of Clone Jutsu, a secret art that creates copies of his body. On a number line, there are $N$ copies of Takahashi, numbered $1$ through $N$. The $i$\\-th copy is located at posit",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc015_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi is an expert of Clone Jutsu, a secret art that creates copies of his body.\nOn a number line, there are $N$ copies of Takahashi, numbered $1$ through $N$. The $i$\\-th copy is located at posit...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments