Neon Pac

Build a tiny browser game called "Neon Pac".

Game spec
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A pac-man style dot-maze chase. Steer a glowing yellow chomper through a 18-by-15 neon labyrinth with the arrow keys, WASD, a swipe, or the on-screen pad, eating every amber dot; the maze wraps left to right through side tunnels on the middle row. Four ghosts — a red chaser, a pink ambusher four cells ahead of you, a cyan mirror-strategist that reflects the chaser, and an orange wanderer — alternate between corner-scatter and full-chase, and eat power pellets to turn them all blue and fleeing for 8 seconds (6 on medium, under 5 on hard) where they are worth 200, 400, 800 and 1600 in a chain; touching a normal ghost costs a life and resets the positions, and eating the final dot flashes the board and rises a faster next level. Three lives on easy and medium, two on hard; speeds and the scatter/chase rhythm scale with difficulty, shown in the HUD. Arcade-night look: a glowing indigo maze outline on near-black, amber dots, pulsing pink pellets, a chomping yellow pac, classic red/pink/cyan/orange ghosts with wobbling skirts, a score/hi/level HUD and a start and game-over screen with a retry (Space, Enter or tap).

Hard constraints — the game will be embedded in a sandboxed iframe on a static gallery site, and a headless browser will screenshot it:

1. Output exactly ONE self-contained HTML file. All CSS and JS inline. Zero external requests: no CDNs, no external fonts, images, or sounds, no fetch/XHR/WebSocket. Any sound must be synthesized with WebAudio.
2. The iframe sandbox is "allow-scripts allow-pointer-lock" (plus an autoplay permission). So: no localStorage, cookies, or indexedDB (opaque origin — access throws); no popups, window.open, or navigation; no access to the parent page; alert()/prompt()/confirm() are silently blocked.
3. The playfield must be visible within 800 ms of load — that is when the screenshot is taken. No dead white screen. If there is a start screen, make it visually rich.
4. Controls: keyboard AND mouse must both work, plus on-screen touch buttons for phones. Call preventDefault() on game keys (arrows, space) so the page never scrolls.
5. The view is 16:9 and must scale to fill the viewport with no overflow or scrollbars.
6. Show a visible score. If the genre has a losing state, show a game-over screen with a restart (button and a key). Idle/clicker games skip game over but still need clear numeric feedback.
7. If you track a score, report it to the arcade shell so the player's best is remembered between visits: on every score change, call parent.postMessage({ source: "ai-arcade", type: "score", score: <number> }, "*"). It is safe to call it no matter what the parent does with it.
8. Keep it tiny: aim for under 400 lines, 60 fps, no frameworks. That 400-line target does not apply to 3D games — true 3D (a camera and perspective-projected world) or pseudo-3D (projected road/track, depth-sorted sprites) — which need their own software renderer and typically land at 800–1400 lines. The rest of this constraint still binds every game: 60 fps, no frameworks, no external assets, and no padding to reach a length.
9. Difficulty: the arcade shell passes the player's chosen difficulty as a URL query parameter. Read it with new URLSearchParams(location.search).get("difficulty") — the value is "easy", "medium", or "hard" (missing or unknown means "medium"). Make the three levels meaningfully different — speed, lives, enemy pressure, reaction time, whatever fits the genre; clicker/idle games with no losing state use starting resources and upgrade cost curves instead. Show the active level in the HUD. Without the parameter the game must be fully playable at its default (medium) tuning.

Return only the complete HTML file, no commentary.