More Realistic Manhattan Distance

AtCoder

IDexawizards2019_f

Time4000ms

Memory256MB

Difficulty—

In Takaha-shi, the capital of Republic of AtCoder, there are $N$ roads extending east and west, and $M$ roads extending north and south. There are no other roads. The $i$\-th east-west road from the north and the $j$\-th north-south road from the west cross at the intersection $(i, j)$. Two east-west roads do not cross, nor do two north-south roads. The distance between two adjacent roads in the same direction is $1$. Each road is one-way; one can only walk in one direction. The permitted direction for each road is described by a string $S$ of length $N$ and a string $T$ of length $M$, as follows: * If the $i$\-th character in $S$ is `W`, one can only walk westward along the $i$\-th east-west road from the north; * If the $i$\-th character in $S$ is `E`, one can only walk eastward along the $i$\-th east-west road from the north; * If the $i$\-th character in $T$ is `N`, one can only walk northward along the $i$\-th north-south road from the west; * If the $i$\-th character in $T$ is `S`, one can only walk southward along the $i$\-th south-west road from the west. Process the following $Q$ queries: * In the $i$\-th query, $a_i, b_i, c_i$ and $d_i$ are given. What is the minimum distance to travel to reach the intersection $(c_i, d_i)$ from the intersection $(a_i, b_i)$ by walking along the roads? ## Constraints * $2 \leq N \leq 100000$ * $2 \leq M \leq 100000$ * $2 \leq Q \leq 200000$ * $|S| = N$ * $S$ consists of `W` and `E`. * $|T| = M$ * $T$ consists of `N` and `S`. * $1 \leq a_i \leq N$ * $1 \leq b_i \leq M$ * $1 \leq c_i \leq N$ * $1 \leq d_i \leq M$ * $(a_i, b_i) \neq (c_i, d_i)$ ## Input Input is given from Standard Input in the following format: $N$ $M$ $Q$ $S$ $T$ $a_1$ $b_1$ $c_1$ $d_1$ $a_2$ $b_2$ $c_2$ $d_2$ $:$ $a_Q$ $b_Q$ $c_Q$ $d_Q$ [samples]

Samples

Input #1

Output #1

6
11
5
4

The permitted direction for each road is shown in the following figure (north upward):
![image](https://img.atcoder.jp/exawizards2019/bfb8c54cc4098353946320d8c263807e.png)
For each of the four queries, a route that achieves the minimum travel distance is as follows:
![image](https://img.atcoder.jp/exawizards2019/d1918596004a23a20aa138e591e0ee99.png)

Input #2

3 3 2
EEE
SSS
1 1 3 3
3 3 1 1

Output #2

4
-1

The travel may be impossible.

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "More Realistic Manhattan Distance",
    "description": {
      "content": "In Takaha-shi, the capital of Republic of AtCoder, there are $N$ roads extending east and west, and $M$ roads extending north and south. There are no other roads. The $i$\\-th east-west road from the n",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 4000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "exawizards2019_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "In Takaha-shi, the capital of Republic of AtCoder, there are $N$ roads extending east and west, and $M$ roads extending north and south. There are no other roads. The $i$\\-th east-west road from the n...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments