Cliff Crew

Build a tiny browser game called "Cliff Crew".

Game spec
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A Lemmings-style skill-assignment puzzler in one self-contained canvas file: a tile grid (50x28, 16px tiles) of dirt, water, a spawn door and an exit door. Lemmings spawn on a timer, walk at a constant pace, turn at walls, fall under gravity, and die on a fall past a pixel threshold or on any contact with water — they never stop walking, so the player must act. Click (or tap) a lemming with a skill selected to spend it: DIG eats the cell below and sinks safely through dirt, BASH tunnels horizontally, BLOCK stands still and turns bumping walkers around, FLOAT disarms the lethal-fall check for one descent, BRIDGE walks forward laying up to six floor cells beneath its feet to span water and gaps. A toolbelt shows each skill with its remaining count, keys 1-5 select, R retries. Three hand-authored levels (float-and-bridge canyon, dig-a-shaft mesa, bridge-the-fjord-and-bash-the-wall) end when every lemming is saved or lost; the run wins at a save quota, score = saved x 100 + unused skills x 25, posted to the parent. Difficulty scales skill counts, spawn rate and the save quota, shown in the HUD.

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.