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Create a responsive browser game titled "지식 수호대" (Knowledge Guardians), a simple educational pixel-art tower-defense game in Korean. Use a full-screen canvas inside a centered app area (maximum width about 1100px) with a teal/mint grassy background, scattered small pixel flecks, crisp hard-edged shapes, dark navy outlines, cream panels, and yellow highlights. Keep the visual style intentionally pixelated/low-resolution with square corners and offset dark drop shadows on UI cards and buttons. On launch, show a semi-transparent dark overlay over the map and a centered cream modal card with a thick dark-navy border and offset shadow. Display the large title "지식 수호대", the message "문제를 풀어 지식 코인을 모으고\n몬스터가 기지에 닿기 전에 막아내세요!", and a yellow "게임 시작" button. Clicking it hides the modal, creates the first math question, and begins the first wave. The playfield is a top-down, fixed-camera map scaled to the viewport. Draw a winding tan road/path as thick square-segment lines through these normalized waypoints: (8%,58%) to (22%,58%), up to (22%,32%), right to (45%,32%), down to (45%,68%), right to (68%,68%), up to (68%,42%), and right to (90%,42%). Use a dark tan broad road with a lighter cream/tan center line. At the final endpoint, draw a small dark-blue base/fortification with a yellow front and two red pixel windows. Place seven square tower slots beside the road at normalized positions approximately (15%,72%), (32%,20%), (38%,48%), (55%,82%), (59%,52%), (78%,58%), and (80%,28%). An empty slot is a translucent cream square with a dark outline and a small pale placeholder icon. Clicking/tapping within roughly 32 pixels of a slot builds a tower if the player has at least 20 knowledge coins; clicking an occupied slot upgrades it for 15 coins. Alternate tower slots should create two tower types: type 1 yellow towers and type 2 lavender towers. Render built towers as colored 30px square blocks with a dark top protrusion/light cap and a "Lv1", "Lv2", etc. label beneath. Towers automatically target the first enemy within approximately 155 pixels plus 8 pixels per level, fire visible small pale-yellow square projectiles, and deal damage. Type 1 fires more quickly and normally deals 2 damage plus level scaling; type 2 fires more slowly and normally deals 1 damage plus level scaling. Upgrade levels improve damage and firing cooldown. Enemies enter at the first waypoint and follow the road segment by segment toward the base. Spawn 3 plus the ceiling of 1.2 times the wave number, one enemy every 0.65 seconds. Give each enemy at least 3 hit points, with health increasing by roughly 0.65 per wave, and movement speed around 0.045 normalized path progress per update with a small wave-based increase. Render enemies as 26px square monsters: mostly coral/pink or orange variants, with dark square eyes and a dark mouth, plus a dark health-bar backing and a mint health fill above them. When a monster reaches the base, subtract one base/life and remove it. If base reaches zero, stop the game and show the Korean failure message "기지가 무너졌어요. 처음부터 버튼으로 다시 도전하세요." in the tip area. When enemies are defeated, increment score and award 5 coins. Include a pointer/touch-friendly HUD over the canvas. Along the top, show dark-outlined cream badges with offset shadows for "🪙 지식 코인" and its value, "❤️ 기지" and its value, and "🌊 웨이브" and its value, followed by buttons "다음 웨이브" and "처음부터". Start the displayed state with the visible initial values matching the interface: 80 knowledge coins, 10 base health, and wave 1. (The implementation may use its own initialized values but should preserve this visible starting presentation.) The next-wave button starts a wave only when no current enemies remain and no enemies are queued; otherwise show "현재 웨이브를 먼저 끝내 주세요.". When a wave is completely cleared, advance the wave number automatically. The reset button reloads/restarts the game. At the bottom-right, show a cream quiz panel with a thick dark outline and shadow. Initially say "문제를 풀어 코인을 얻고, 길 옆 빈 칸을 눌러 타워를 지으세요." and show the tip "타워는 자동으로 적을 공격합니다. 정답을 맞히면 +20 코인!". After starting, present one randomly selected multiple-choice question in Korean, with four answers in a 2-column grid. Use exactly this question pool and correct choices: "3 × 4 = ?" answers ["7","12","14","16"] correct "12"; "0.5는 분수로?" ["1/2","1/3","2/5","5/2"] correct "1/2"; "1/4 + 1/4 = ?" ["1/8","1/2","2/4","3/4"] correct "1/2"; "10의 30%는?" ["1","3","5","30"] correct "3"; "2.5 + 1.5 = ?" ["3","4","4.5","5"] correct "4"; "6 × 7 = ?" ["36","40","42","48"] correct "42"; "1m는 몇 cm?" ["10","50","100","1000"] correct "100"; and "12 ÷ 3 = ?" ["3","4","6","9"] correct "4". Selecting a correct answer awards 25 coins and immediately replaces it with another random question, with the message "정답! +25 지식 코인. 타워를 짓거나 업그레이드해 보세요." in green. A wrong answer gives no coins, replaces the question, and shows "아쉬워요. 다시 생각해 보고 다음 문제에 도전하세요." in orange/red. At the bottom-left, show a smaller cream instructional card (hide it on narrow mobile widths) reading "📚 학습 목표\n분수·소수·곱셈 문제를 풀며 자원을 모으고, 전략적으로 타워를 배치해 보세요.". Make the entire layout responsive: on small screens use smaller badges/buttons, allow the top row to wrap, make the quiz panel nearly full width at the bottom, and hide the learning-goal card. Use Korean system sans-serif typography, dark navy text, cream backgrounds, mint accent colors, coral error colors, and touch-friendly buttons. Do not add unrelated modes or mechanics; the central loop is answer math questions for coins, place/upgrade towers beside the winding path, and automatically defend the base against successive enemy waves.