Beacon Relay

Build a tiny browser game called "Beacon Relay".

Game spec
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A semaphore line across a chain of hills, and you are the station that has to pass the message on. A flag pair sits on your tower and a distant neighbour posts a symbol by setting its two arms to positions; you must read the symbol and reproduce it exactly on your own tower before the fog closes, then the next symbol arrives. The reading is the game: the neighbour is far away, so the arms are small, and fog, sun glare and weather wash the picture out, so you squint and check rather than guess. Click or tap an arm to rotate it, or press the arrow keys to select and rotate; a match checker lights when both arms agree with what you think you saw, and confirming a wrong symbol sends a false message down the line and costs a codebook. Reading speed is worth more than certainty, and a spyglass (Space) steadies the image for a moment at the cost of time. Each correct relay pays by how fast and how little glass you used, then symbols get shorter-lived and the weather gets worse; three false messages ends the watch, and difficulty sets fog density, glare, symbol lifetime and how similar the confusable pairs are. Signal-hill look: layered blue-green ridges in haze, a wooden station tower with a lattice frame, two black semaphore arms with brass joints, a brass spyglass, drifting cloud banks, and a wind hiss with a wooden clack as the arms move in WebAudio.

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.