Lazzie wandered off and now can't find her way home. Please, help this silly cat.

# The Goal

Direct Lazzie to safely reach home.

# Rules

Lazzie walks on a grid containing passable tiles and various obstacles, and can move in cardinal directions: N, S, W, E. She can't see the entire map, only a small area around her, but she remembers where, relative to her starting position, the home is. Lazzie is a very fragile being, so colliding with any obstacle results in her death.

Victory Conditions

- Lazzie reaches a home entrance within a test-dependent turn limit.

Loss Conditions

- Lazzie steps into an obstacle.
- Number of turns exceeds test's turn limit.
- The answer is not properly formatted.
- Response time exceeds the time limit.

### 🐞 Debugging tips

- Move map around and zoom in/out using mouse drag and wheel.
- Print more than one action (up to 10) to show visualized future path.

# Game Input

Initial input

A single line containing three space-separated integers, visionRange homeDistanceHorizontal homeDistanceVertical, where

- visionRange is a diameter of Lazzie's vision (always odd),
- homeDistanceHorizontal is a distance in W/E direction towards home (negative means W side, positive means E side),
- homeDistanceVertical is a distance in N/S direction towards home (negative means N side, positive means S side).

Input for the following turns
visionRange lines: a string of length visionRange, containing a row of the map within the vision range (top to bottom). Possible values:

- L Lazzie (always present in the center tile),
- H home entrance,
- . passable terrain,
- # impassable obstacle,
- ? outside vision circle.

Output
A single line containing a direction(s) where Lazzie should go: N/S/W/E. The first provided direction is applied, but more can be given to show planned path on visualization (max 10 steps is visualized).
Constraints
10 ≤ map width, map height ≤ 200
5 ≤ visionRange ≤ 13
A turn limit is usually 500, but can be lower (down to 350) depending on the potential replay size
Response time for first turn ≤ 1s
Response time for the following turns ≤ 50ms