Dice Cascade

Build a tiny browser game called "Dice Cascade".

Game spec
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A five-dice Yahtzee-style roll. Press the button, click, or hit Space to roll; click individual dice to hold them, then roll the rest, on a roll budget that tightens with difficulty (4 rolls on easy, 3 on medium, 2 on hard). A scorecard of nine categories on the right — ones through sixes counting only that face, one N-of-a-Kind row that scores all dice when at least N dice agree (N=3 on easy and medium, 4 on hard), Chance summing all dice, and Yahtzee for five of a kind paying 60 on easy, 50 on medium and 40 on hard — lets you click any still-empty category to bank the score for the current dice, after which that row greys out. A Yahtzee banked in the Yahtzee row lets later live Yahtzees add a difficulty-scaled bonus to another category. Nine hands, one per category, end the game with a totals card, a high score and a REPLAY button. HUD shows hand number, rolls left and running total. Difficulty sets the roll budget, the N-of-a-Kind threshold, the Yahtzee pay, a minimum dice-sum gate on N-of-a-Kind and Chance, and whether the Yahtzee bonus exists at all.

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.