Push and Carry

AtCoder

IDabc323_f

Time2000ms

Memory256MB

Difficulty—

Takahashi and a cargo are on a coordinate plane. Takahashi is currently at $(X_A,Y_A)$, and the cargo is at $(X_B,Y_B)$. He wants to move the cargo to $(X_C,Y_C)$. When he is at $(x,y)$, he can make one of the following moves in a single action. * Move to $(x+1,y)$. If the cargo is at $(x+1,y)$ before the move, move it to $(x+2,y)$. * Move to $(x-1,y)$. If the cargo is at $(x-1,y)$ before the move, move it to $(x-2,y)$. * Move to $(x,y+1)$. If the cargo is at $(x,y+1)$ before the move, move it to $(x,y+2)$. * Move to $(x,y-1)$. If the cargo is at $(x,y-1)$ before the move, move it to $(x,y-2)$. Find the minimum number of actions required to move the cargo to $(X_C,Y_C)$. ## Constraints * $-10^{17}\leq X_A,Y_A,X_B,Y_B,X_C,Y_C\leq 10^{17}$ * $(X_A,Y_A)\neq (X_B,Y_B)$ * $(X_B,Y_B)\neq (X_C,Y_C)$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $X_A$ $Y_A$ $X_B$ $Y_B$ $X_C$ $Y_C$ [samples]

Samples

Input #1

1 2 3 3 0 5

Output #1

9

Takahashi can move the cargo to $(0,5)$ in nine actions as follows.

*   Move to $(2,2)$.
*   Move to $(3,2)$.
*   Move to $(3,3)$. The cargo moves to $(3,4)$.
*   Move to $(3,4)$. The cargo moves to $(3,5)$.
*   Move to $(4,4)$.
*   Move to $(4,5)$.
*   Move to $(3,5)$. The cargo moves to $(2,5)$.
*   Move to $(2,5)$. The cargo moves to $(1,5)$.
*   Move to $(1,5)$. The cargo moves to $(0,5)$.

It is impossible to move the cargo to $(0,5)$ in eight or fewer actions, so you should print $9$.

Input #2

0 0 1 0 -1 0

Output #2

Input #3

\-100000000000000000 -100000000000000000 100000000000000000 100000000000000000 -100000000000000000 -100000000000000000

Output #3

800000000000000003

API Response (JSON)

{
  "problem": {
    "name": "Push and Carry",
    "description": {
      "content": "Takahashi and a cargo are on a coordinate plane. Takahashi is currently at $(X_A,Y_A)$, and the cargo is at $(X_B,Y_B)$. He wants to move the cargo to $(X_C,Y_C)$. When he is at $(x,y)$, he can make o",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc323_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi and a cargo are on a coordinate plane.\nTakahashi is currently at $(X_A,Y_A)$, and the cargo is at $(X_B,Y_B)$. He wants to move the cargo to $(X_C,Y_C)$.\nWhen he is at $(x,y)$, he can make o...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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