Deep Dug

Build a tiny browser game called "Deep Dug".

Game spec
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A dig-dug style air-and-dirt puzzler. Steer a little blue digger with the arrows, WASD, or taps (8-way: D-pad plus BLOW button on phones) to carve tunnels through a speckled brown dirt field, while the two top rows are open sky. Blobs pop in from the edges — fast pink ones wander the sky, red ones amble through the dirt, and blue ones drill vertical shafts up from the bottom of the grid. Hold Space or Enter to blow air in the direction you're facing: it travels up to three open cells and inflates the first blob it touches until it pops for 100, 200 or 300 points; blobs slowly deflate if you stop blowing. Pop every blob in a level (five to nine depending on difficulty) for a 300 bonus and a meaner next level; a blob that touches you costs a life and restarts the level. Two to three lives depending on difficulty, with brief invulnerability after each hit. Underground night look: speckled dirt cells, dark dug tunnels, a starless blue sky strip, glossy balloon-blobs that crack as they inflate, and a hard-hat digger with a face pack.

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.