Paired Wizards

AtCoder

IDarc142_f

Time3000ms

Memory256MB

Difficulty—

Two wizards, $X$ and $Y$, are fighting with a monster. Initially, each of the wizards has a magic power of $0$. They know the following two spells. * Spell $1$: Increases the caster's magic power by $1$. * Spell $2$: Deals damage equal to the caster's magic power to the monster. After each wizard uses a spell $N$ times, they will withdraw from the battle. For each $i=1, \ldots, N$, they must use one of the following combinations of spells for their $i$\-th spells. * $X$ casts Spell $a_i$, and $Y$ casts Spell $b_i$. * $X$ casts Spell $c_i$, and $Y$ casts Spell $d_i$. Find the maximum total damage that can be dealt to the monster before the withdrawal. ## Constraints * $1 \leq N \leq 8000$ * $a_i,b_i,c_i,d_i \in {1,2}$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $a_1$ $b_1$ $c_1$ $d_1$ $\vdots$ $a_N$ $b_N$ $c_N$ $d_N$ [samples]

Samples

Input #1

Output #1

3

The maximum total damage can be achieved as follows.

*   As the $1$\-st spells, use $a_1=1,\, b_1=1$, increasing both $X$'s and $Y$'s magic powers to $1$.
*   As the $2$\-nd spells, use $c_2=2,\, d_2=2$, dealing $2$ points of damage in total.
*   As the $3$\-rd spells, use $a_3=2,\, b_3=1$, dealing $1$ point of damage by $X$'s spell and increasing $Y$'s magic power to $2$.

Input #2

Output #2

0

Casting Spell $2$ with a magic power of $0$ deals no damage.

Input #3

Output #3

Input #4

Output #4

API Response (JSON)

{
  "problem": {
    "name": "Paired Wizards",
    "description": {
      "content": "Two wizards, $X$ and $Y$, are fighting with a monster. Initially, each of the wizards has a magic power of $0$. They know the following two spells. *   Spell $1$: Increases the caster's magic power b",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc142_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Two wizards, $X$ and $Y$, are fighting with a monster.\nInitially, each of the wizards has a magic power of $0$. They know the following two spells.\n\n*   Spell $1$: Increases the caster's magic power b...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments