1D Matching

AtCoder

IDcf16_exhibition_final_a

Time2000ms

Memory256MB

Difficulty—

#nck { width: 30px; height: auto; }There are $N$ computers and $N$ sockets in a one-dimensional world. The coordinate of the $i$\-th computer is $a_i$, and the coordinate of the $i$\-th socket is $b_i$. It is guaranteed that these $2N$ coordinates are pairwise distinct. Snuke wants to connect each computer to a socket using a cable. Each socket can be connected to only one computer. In how many ways can he minimize the total length of the cables? Compute the answer modulo $10^9+7$. ## Constraints * $1 ≤ N ≤ 10^5$ * $0 ≤ a_i, b_i ≤ 10^9$ * The coordinates are integers. * The coordinates are pairwise distinct. ## Input The input is given from Standard Input in the following format: $N$ $a_1$ : $a_N$ $b_1$ : $b_N$ [samples]

Samples

Input #1

Output #1

2

There are two optimal connections: $0-20, 10-30$ and $0-30, 10-20$. In both connections the total length of the cables is $40$.

Input #2

Output #2

API Response (JSON)

{
  "problem": {
    "name": "1D Matching",
    "description": {
      "content": "#nck { width: 30px; height: auto; }There are $N$ computers and $N$ sockets in a one-dimensional world. The coordinate of the $i$\\-th computer is $a_i$, and the coordinate of the $i$\\-th socket is $b_i",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "cf16_exhibition_final_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "#nck { width: 30px; height: auto; }There are $N$ computers and $N$ sockets in a one-dimensional world. The coordinate of the $i$\\-th computer is $a_i$, and the coordinate of the $i$\\-th socket is $b_i...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments