Hammer 2

AtCoder

IDabc273_f

Time3000ms

Memory256MB

Difficulty—

Takahashi is at the origin of a number line. Takahashi wants to reach the goal at coordinate $X$. Also, there are $N$ walls and $N$ hammers on the number line. * At coordinates $Y_1,Y_2,\dots,Y_N$ are walls of types $1,2,\dots,N$, respectively. * Initially, Takahashi cannot get over the walls. * At coordinates $Z_1,Z_2,\dots,Z_N$ are hammers of types $1,2,\dots,N$, respectively. * When he arrives at a coordinate with a hammer, he obtains the hammer. * The hammer of type $i$ is dedicated to destroying the wall of type $i$. After he obtains the hammer of type $i$, he can destroy the wall of type $i$ and get over it. Determine if he can reach the goal. If he can, find the minimum distance he travels. ## Constraints * All values in the input are integers. * $1 \le N \le 1500$ * $1 \le |X|,|Y_i|,|Z_i| \le 10^9$ * The $(2 \times N + 1)$ coordinates $X,Y_i$ and $Z_i$ are distinct. ## Input The input is given from Standard Input in the following format: $N$ $X$ $Y_1$ $Y_2$ $\dots$ $Y_N$ $Z_1$ $Z_2$ $\dots$ $Z_N$ [samples]

Samples

Input #1

3 10
-2 8 -5
5 -10 3

Output #1

40

Takahashi can reach the goal by traveling a distance of $40$ as follows, which is the minimum possible:

*   He starts at coordinate $0$.
*   He moves to coordinate $3$ to obtain the hammer of type $3$.
*   He moves to coordinate $5$ to obtain the hammer of type $1$.
*   He moves to coordinate $-2$ to destroy the wall of type $1$.
*   He moves to coordinate $-5$ to destroy the wall of type $3$.
*   He moves to coordinate $-10$ to obtain the hammer of type $2$.
*   He moves to coordinate $8$ to destroy the wall of type $2$.
*   He moves to coordinate $10$, which is the goal.

Input #2

5 -1
10 -20 30 -40 50
-10 20 -30 40 -50

Output #2

1

It may not be required that he obtains a hammer or destroys a wall to reach the goal.

Input #3

1 100
30
60

Output #3

\-1

Takahashi cannot obtain the hammer of type $1$, and neither can he reach the goal.

Input #4

4 865942261
703164879 -531670946 -874856231 -700164975
-941120316 599462305 -649785130 665402307

Output #4

4078987507

API Response (JSON)

{
  "problem": {
    "name": "Hammer 2",
    "description": {
      "content": "Takahashi is at the origin of a number line. Takahashi wants to reach the goal at coordinate $X$. Also, there are $N$ walls and $N$ hammers on the number line. *   At coordinates $Y_1,Y_2,\\dots,Y_N$ ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc273_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi is at the origin of a number line. Takahashi wants to reach the goal at coordinate $X$.\nAlso, there are $N$ walls and $N$ hammers on the number line.\n\n*   At coordinates $Y_1,Y_2,\\dots,Y_N$ ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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