Collision 2

AtCoder

IDabc243_c

Time2000ms

Memory256MB

Difficulty—

There are $N$ people in an $xy$\-plane. Person $i$ is at $(X_i, Y_i)$. The positions of all people are different. We have a string $S$ of length $N$ consisting of `L` and `R`. If $S_i =$ `R`, Person $i$ is facing right; if $S_i =$ `L`, Person $i$ is facing left. All people simultaneously start walking in the direction they are facing. Here, right and left correspond to the positive and negative $x$\-direction, respectively. For example, the figure below shows the movement of people when $(X_1, Y_1) = (2, 3), (X_2, Y_2) = (1, 1), (X_3, Y_3) =(4, 1), S =$ `RRL`. ![image](https://img.atcoder.jp/ghi/f33104f8bc05a920f2b74ead8ad1e3d2.png) We say that there is a collision when two people walking in opposite directions come to the same position. Will there be a collision if all people continue walking indefinitely? ## Constraints * $2 \leq N \leq 2 \times 10^5$ * $0 \leq X_i \leq 10^9$ * $0 \leq Y_i \leq 10^9$ * $(X_i, Y_i) \neq (X_j, Y_j)$ if $i \neq j$. * All $X_i$ and $Y_i$ are integers. * $S$ is a string of length $N$ consisting of `L` and `R`. ## Input Input is given from Standard Input in the following format: $N$ $X_1$ $Y_1$ $X_2$ $Y_2$ $\vdots$ $X_N$ $Y_N$ $S$ [samples]

Samples

Input #1

Output #1

Yes

This input corresponds to the example in the Problem Statement.  
If all people continue walking, Person $2$ and Person $3$ will collide. Thus, `Yes` should be printed.

Input #2

Output #2

No

Since Person $1$ and Person $2$ walk in the same direction, they never collide.

Input #3

Output #3

Yes

API Response (JSON)

{
  "problem": {
    "name": "Collision 2",
    "description": {
      "content": "There are $N$ people in an $xy$\\-plane. Person $i$ is at $(X_i, Y_i)$. The positions of all people are different. We have a string $S$ of length $N$ consisting of `L` and `R`.   If $S_i =$ `R`, Person",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc243_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ people in an $xy$\\-plane. Person $i$ is at $(X_i, Y_i)$. The positions of all people are different.\nWe have a string $S$ of length $N$ consisting of `L` and `R`.  \nIf $S_i =$ `R`, Person...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments