Colorful Balls

AtCoder

IDagc012_d

Time2000ms

Memory256MB

Difficulty—

Snuke arranged $N$ colorful balls in a row. The $i$\-th ball from the left has color $c_i$ and weight $w_i$. He can rearrange the balls by performing the following two operations any number of times, in any order: * Operation $1$: Select two balls with the same color. If the total weight of these balls is at most $X$, swap the positions of these balls. * Operation $2$: Select two balls with different colors. If the total weight of these balls is at most $Y$, swap the positions of these balls. How many different sequences of colors of balls can be obtained? Find the count modulo $10^9 + 7$. ## Constraints * $1 ≤ N ≤ 2 × 10^5$ * $1 ≤ X, Y ≤ 10^9$ * $1 ≤ c_i ≤ N$ * $1 ≤ w_i ≤ 10^9$ * $X, Y, c_i, w_i$ are all integers. ## Input Input is given from Standard Input in the following format: $N$ $X$ $Y$ $c_1$ $w_1$ $:$ $c_N$ $w_N$ [samples]

Samples

Input #1

Output #1

2

*   The sequence of colors $(2,4,3,4)$ can be obtained by swapping the positions of the first and third balls by operation $2$.
*   It is also possible to swap the positions of the second and fourth balls by operation $1$, but it does not affect the sequence of colors.

Input #2

1 1 1
1 1

Output #2

Input #3

Output #3

129729600

API Response (JSON)

{
  "problem": {
    "name": "Colorful Balls",
    "description": {
      "content": "Snuke arranged $N$ colorful balls in a row. The $i$\\-th ball from the left has color $c_i$ and weight $w_i$. He can rearrange the balls by performing the following two operations any number of times, ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc012_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Snuke arranged $N$ colorful balls in a row. The $i$\\-th ball from the left has color $c_i$ and weight $w_i$.\nHe can rearrange the balls by performing the following two operations any number of times, ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments