7

AtCoder

IDabc225_e

Time2000ms

Memory256MB

Difficulty—

There are $N$ 7's drawn in the first quadrant of a plane. The $i$\-th 7 is a figure composed of a segment connecting $(x_i-1,y_i)$ and $(x_i,y_i)$, and a segment connecting $(x_i,y_i-1)$ and $(x_i,y_i)$. You can choose zero or more from the $N$ 7's and delete them. What is the maximum possible number of 7's that are wholly visible from the origin after the optimal deletion? Here, the $i$\-th 7 is wholly visible from the origin if and only if: * the interior (excluding borders) of the quadrilateral whose vertices are the origin, $(x_i-1,y_i)$, $(x_i,y_i)$, $(x_i,y_i-1)$ does not intersect with the other 7's. ## Constraints * $1 \leq N \leq 2 \times 10^5$ * $1 \leq x_i,y_i \leq 10^9$ * $(x_i,y_i) \neq (x_j,y_j)\ (i \neq j)$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $x_1$ $y_1$ $x_2$ $y_2$ $\hspace{0.45cm}\vdots$ $x_N$ $y_N$ [samples]

Samples

Input #1

Output #1

2

If the first 7 is deleted, the other two 7's ― the second and third ones ― will be wholly visible from the origin, which is optimal.
If no 7's are deleted, only the first 7 is wholly visible from the origin.

Input #2

10
414598724 87552841
252911401 309688555
623249116 421714323
605059493 227199170
410455266 373748111
861647548 916369023
527772558 682124751
356101507 249887028
292258775 110762985
850583108 796044319

Output #2

10

It is best to keep all 7's.

API Response (JSON)

{
  "problem": {
    "name": "7",
    "description": {
      "content": "There are $N$ 7's drawn in the first quadrant of a plane. The $i$\\-th 7 is a figure composed of a segment connecting $(x_i-1,y_i)$ and $(x_i,y_i)$, and a segment connecting $(x_i,y_i-1)$ and $(x_i,y_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": "abc225_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ 7's drawn in the first quadrant of a plane.\nThe $i$\\-th 7 is a figure composed of a segment connecting $(x_i-1,y_i)$ and $(x_i,y_i)$, and a segment connecting $(x_i,y_i-1)$ and $(x_i,y_i...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments