⣿⣿⣿⣿⣟⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿
⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⢀⣰⣶⣶⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢻
⣿⣿⣿⠁⠄⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽
⣿⣿⡏⣸⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠰
⣿⣿⡇⠁⠀⠀⠀⣤⣍⣙⣿⣿⣏⣠⠄⠲⠲⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣿⣿⠁⠀⠀⠀⠀⠀⢤⠙⣿⣿⣿⣇⣀⡐⢂⣠⡄⠠⠀⠀⠀⠀⠀⠀⡀⢠⢸
⣿⣿⠀⠀⠐⠀⣶⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⠈⠀⠀⠀⠉⠘⣼
⣿⣿⠀⠈⠀⠀⣿⣿⣿⡿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣧⡀⠀⢄⠲⠀⠀⠀⣱
⣿⣿⡆⠀⠀⠀⠈⣿⣿⣷⣶⣼⣾⣿⣿⣿⣿⣿⣿⣿⣷⠂⠀⠀⠂⢀⢲
⣿⣿⣿⡆⠀⠀⠀⠙⣿⠋⠠⠄⢀⠉⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣦⠀⠀⠀⠘⣿⣤⣤⣶⣿⣿⣿⣿⣿⠟⣛⡽⠀⠀⠀⠠⣸
⣿⣿⣿⣿⣿⣷⡀⠀⠀⠈⠻⣿⣿⣿⠿⠛⠋⠐⠚⠛⠃

⠀⠀⣞⢽⢪⢣⢣⢣⢫⡺⡵⣝⡮⣗⢷⢽⢽⢽⣮⡷⡽⣜⣜⢮⢺⣜⢷⢽⢝⡽⣝
⠸⡸⠜⠕⠕⠁⢁⢇⢏⢽⢺⣪⡳⡝⣎⣏⢯⢞⡿⣟⣷⣳⢯⡷⣽⢽⢯⣳⣫⠇
⠀⠀⢀⢀⢄⢬⢪⡪⡎⣆⡈⠚⠜⠕⠇⠗⠝⢕⢯⢫⣞⣯⣿⣻⡽⣏⢗⣗⠏
⠀⠪⡪⡪⣪⢪⢺⢸⢢⢓⢆⢤⢀⠀⠀⠀⠀⠈⢊⢞⡾⣿⡯⣏⢮⠷⠁
⠀⠀⠀⠈⠊⠆⡃⠕⢕⢇⢇⢇⢇⢇⢏⢎⢎⢆⢄⠀⢑⣽⣿⢝⠲⠉
⠀⠀⠀⠀⠀⡿⠂⠠⠀⡇⢇⠕⢈⣀⠀⠁⠡⠣⡣⡫⣂⣿⠯⢪⠰⠂
⠀⠀⠀⠀⡦⡙⡂⢀⢤⢣⠣⡈⣾⡃⠠⠄⠀⡄⢱⣌⣶⢏⢊⠂
⠀⠀⠀⠀⢝⡲⣜⡮⡏⢎⢌⢂⠙⠢⠐⢀⢘⢵⣽⣿⡿⠁⠁
⠀⠀⠀⠀⠨⣺⡺⡕⡕⡱⡑⡆⡕⡅⡕⡜⡼⢽⡻⠏⠀
⠀⠀⠀⠀⣼⣳⣫⣾⣵⣗⡵⡱⡡⢣⢑⢕⢜⢕⡝⠀
⠀⠀⠀⣴⣿⣾⣿⣿⣿⡿⡽⡑⢌⠪⡢⡣⣣⡟⠀
⠀⠀⠀⡟⡾⣿⢿⢿⢵⣽⣾⣼⣘⢸⢸⣞⡟⠀
⠀⠀⠀⠀⠁⠇⠡⠩⡫⢿⣝⡻⡮⣒⢽⠋

⠄⡄⡆⡄⠄⠄⠄⠄⠄⢀⡤⠄⠒⠄⠄⠄⣄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣄⣠⠄
⢱⣼⣿⠇⢀⠄⠄⠄⡰⠅⢀⣴⣾⡿⠿⢷⠝⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣿⣿⡝
⠸⣿⣿⠗⠋⠄⠄⠠⠂⠄⣿⣿⡧⢒⣂⣼⣿⣄⡚⡄⠄⠄⠄⠄⠄⠈⠲⣿⣿⡯
⠄⣿⡿⠄⠄⠄⠄⠄⠄⠄⣿⣿⣿⣿⡏⣩⣤⣵⡠⡺⡄⠄⠄⠄⠄⠄⠄⢸⣿⠃
⠄⣿⣿⠄⠄⠄⠄⠄⢀⢀⡘⣿⣿⣿⣧⠋⠖⠚⠂⢹⣿⠄⠄⠄⠄⠄⠄⣾⣿⠄
⠄⣿⣷⡇⠄⠄⠄⠄⢁⣏⣷⣿⣿⣿⣿⣿⣿⣟⡲⠾⢻⠄⠄⠄⠄⠄⣸⣿⡟⠄
⠄⢹⣿⣿⡀⠄⠄⠄⠄⠉⢫⣼⣿⣿⣿⣿⣿⠟⠓⠓⡘⠄⠄⠄⠄⣰⣿⣿⠁⠄
⠄⠈⠿⠿⠿⠄⠄⠄⠄⠄⠄⠻⠿⠿⠿⠟⠉⠄⠄⠹⠇⠄⠄⠄⠺⠿⠿⠏⠄⠄

⠀⣤⣤⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⣻⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠛⠿⠛⢁⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢹⣿⣁⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆⠀⠀
⢠⣶⣤⣄⠀⠀⠀⠙⠛⠋⢠⣤⡀⠀⠀⠀⠀⠀⠀⣼⡟⣾⠀⠀
⣾⡏⣸⡿⠀⠀⠀⠀⠀⠀⠈⣿⡛⠷⣦⣤⣀⡀⣴⡟⠀⢻⣧⠀
⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠉⠙⠻⠟⠀⠀⠈⣿⡄
⠀⠀⠀⠀⢰⣦⣤⣤⣤⣄⣀⣯⠇⠀⠀⠀⠀⢀⣠⣤⣴⡶⠿⠇
⠀⠀⠀⠀⠈⢻⣦⡉⠉⠉⠛⠋⠀⢀⣠⣴⡾⠛⠋⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⢀⣠⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀

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$$$__$$$$$$$$$$$$$$$$$$$$$$_$$ $
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⣀⡀
⠀⠀⠀⠀⣿⠙⣦⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠁
⠀⠀⠀⠀⢻⠀⠈⠳⠀⠀⣀⣴⡾⠛⠁⣠⠂⢠⠇
⠀⠀⠀⠀⠈⢀⣀⠤⢤⡶⠟⠁⢀⣴⣟⠀⠀⣾
⠀⠀⠀⠠⠞⠉⢁⠀⠉⠀⢀⣠⣾⣿⣏⠀⢠⡇
⠀⠀⡰⠋⠀⢰⠃⠀⠀⠉⠛⠿⠿⠏⠁⠀⣸⠁
⠀⠀⣄⠀⠀⠏⣤⣤⣀⡀⠀⠀⠀⠀⠀⠾⢯⣀
⠀⠀⣻⠃⠀⣰⡿⠛⠁⠀⠀⠀⢤⣀⡀⠀⠺⣿⡟⠛⠁
⠀⡠⠋⡤⠠⠋⠀⠀⢀⠐⠁⠀⠈⣙⢯⡃⠀⢈⡻⣦
⢰⣷⠇⠀⠀⠀⢀⡠⠃⠀⠀⠀⠀⠈⠻⢯⡄⠀⢻⣿⣷
⠀⠉⠲⣶⣶⢾⣉⣐⡚⠋⠀⠀⠀⠀⠀⠘⠀⠀⡎⣿⣿⡇
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⡄⠀⠀⢠⣿⣴⠀⠀⣿⣿⣿⣧
⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠇⠀⢠⠟⣿⠏⢀⣾⠟⢸⣿⡇
⠀⠀⢠⣿⣿⣿⣿⠟⠘⠁⢠⠜⢉⣐⡥⠞⠋⢁⣴⣿⣿⠃
⠀⠀⣾⢻⣿⣿⠃⠀⠀⡀⢀⡄⠁⠀⠀⢠⡾
⠀⠀⠃⢸⣿⡇⠀⢠⣾⡇⢸⡇⠀⠀⠀⡞
⠀⠀⠀⠈⢿⡇⡰⠋⠈⠙⠂⠙⠢
⠀⠀⠀⠀⠈⢧