Heavy Firearm Emojis & Text

Copy & Paste Heavy Firearm Emojis & Symbols ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⢠⣦⣤⣶⣾⣽⣯⣭⣭⣽⣯⣭⣿⣯⣿⣽⣿⣿⣿⣿⣿⣷⣯⣧⣴⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⣀⡀ ⢐⣶⣶⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡭⣕⣥⣦⣤⣵⣴⣤⡊⣷⣜⣷⢢⣶⡴⠴⢮⣊⢓⣴⣶⣾⣿⣿⡓⣿⡿⢿⢯⣯⣽⡹⠟⠻⠿⢛⠟⡛⢻⣿⣿⣿⣟⡿⢟⣻⠻⣿⣷⣴⢦⠤⢤⡤⢤⣴⣶⣿⡿⣿⣮⢹⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⣻⣿⣭⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣿⣿⡻⣯⢱⣿⢙⣿⣿⢝⣿⡿⢀⣀⡈⢠⡻⢍⠀⠠⡂⣳⣿⣿⣟⣿⣟⣅⣿⣇⣧⠠⡈⣷⣷⢫⠚⡆⣶⡌⠙⡏⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠘⠓⠒⠗⠒⠒⠒⠚⠛⠒⣻⣿⢿⠵⡒⠍⢎⡉⠓⡖⣇⣿⣗⣾⣚⣿⣛⣿⣾⣿⣿⣾⣷⣶⣶⣿⣿⣾⣿⢿⠋⠛⠛⠛⠛⠛⠚⠞⠚⠓⠒⠯⣰⠸⣧⢀⠃⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠚⠍⠞⠀⠀⠁⠈⣿⣿⣿⣽⣿⠿⣿⣿⠛⠛⣿⣿⣯⣿⣿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠟⢛⣳⣄⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⡏⠙⠠⠤⠯⠑⢛⣵⣟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣿⣿⣿⣯⣇⠀⠀⠀⠀⠀⠈⢒⡿⡯⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠙⡍⠏⡯⣧⠀⠀⠀⠀⠀⠀⠈⣾⣿⠽⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣖⣃⣃⣐⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣌⢁⣰⣴⣰⣲⣲⣰⣠⡠⣤⣤⣰⣬⣩⢿⣿⣻⣿⡿⣹⡿⣿⢿⣿⢛⡛⡛⠛⣛⣿⣿⣿⣿⣷⡖⡤⣤⢤⡤⡤⢤⣶⡾⣶⡞⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣯⣭⠭⡯⢭⡭⡭⡭⣉⣉⣿⠿⣿⠿⣿⡵⡞⣿⣟⢛⣿⣃⢌⣙⡌⡩⠀⣐⣔⣯⣽⣟⣿⣼⣇⣷⢢⡮⠦⠉⡫⠈⠌⣨⢹⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⠷⠿⡵⡡⡠⠃⠏⠷⣾⣿⡾⠿⢿⣿⡿⢷⣿⣿⣯⣷⣿⠿⠏⠉⠉⠉⠉⠉⠉⠉⠉⢷⣧⡿⣟⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⡟⠛⠄⠜⠫⢿⣻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠈⠽⣓⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣈⠎⠉⢻⠀⠀⠀⠀⠀⠘⠛⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣦⣤⣴⣤⣤⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⣿⣦⣀⠀⢀⣀⣀⣏⣹⠀ ⢠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠭⠭⠽⠽⠿⠿⠭⠭⠭⠽⠿⠿⠛ ⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⢻⣿⣿⣿⡟⠏⠉⠉⣿⢿⣿⣿⣿⣇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⢠⣿⣿⣿⠋⠑⠒⠒⠚⠙⠸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢶⣶⣶⠼⣦⣤⣼⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣯⠿⠟⠛⠻⢶⣿⣯⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣺⡿⠿⠷⠶⠒⢶⣶⠖⠀⠉⡻⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⢻⣭⣫⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣖⡿⠋⢙⣿⠿⢿⠿⣿⡦⠄⠀⠀⠀⣠⣾⠟⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣰⣿⣴⣿⡿⠿⠿⠿⢿⣦⣄⠀⠀⠀⣠⣾⣿⠃⠀⢀⣸⡿⣳⣶⣲⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣽⡿⣛⣵⠾⠿⠿⠷⣦⣌⠻⣷⣄⢰⣿⠟⠁⠀⢠⣾⠿⢡⣯⠸⠧⢽⣄⠀⠀⠀⠀⠀ ⠀⢸⡇⡟⣴⡿⢟⣽⣾⣿⣶⣌⠻⣧⣹⣿⡿⠋⠀⠀⠀⣾⠿⡇⣽⣿⣄⠀⠀⠉⠳⣄⢀⡀⠀ ⠀⢸⠇⢳⣿⢳⣿⣿⣿⣿⣿⣿⡆⢹⡇⣿⡇⠀⡆⣠⣼⡏⢰⣿⣿⣿⣿⣦⠀⠀⠀⠈⠳⣅⠀ ⠀⣸⡀⢸⣿⢸⣿⣿⣿⣿⣿⣿⡇⣸⡇⣿⡇⠀⡟⣻⢳⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣧ ⢰⡟⡿⡆⠹⣧⡙⢿⣿⣿⠿⡟⢡⣿⢷⣿⣧⠾⢠⣿⣾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠘ ⠀⠻⡽⣦⠀⠈⠙⠳⢶⣦⡶⠞⢻⡟⡸⠟⠁⢠⠟⠉⠉⠙⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡴ ⠀⠀⢸⣿⡇⠀⠀⣀⣠⠀⢀⡀⠸⣹⠇⠀⣰⡟⡀⠀⠈⠛⠻⢿⣻⣿⡿⠀⠀⠀⠀⠀⠀⡠⠁ ⠀⠀⢸⣿⣇⣴⢿⣿⣿⣿⣮⣿⣷⡟⠀⣰⣿⢰⠀⣀⠀⠀⠀⢀⣉⣿⡇⠀⠀⠀⠀⠀⣸⠃⠀ ⠀⠀⢸⣿⡟⣯⠸⣿⣿⣿⣿⢈⣿⡇⣼⣿⠇⣸⡦⣙⣷⣦⣴⣯⠿⠛⢷⡀⠀⠀⠀⣰⡟⠀⠀ ⠀⠀⠘⣿⣿⡸⣷⣝⠻⠟⢋⣾⣟⣰⡏⣠⣤⡟⠀⠀⠈⠉⠁⠀⠀⠀⠀⢻⣶⠀⢀⣿⠁⠀⠀ ⠀⠀⠀⢸⡿⣿⣦⣽⣛⣛⣛⣭⣾⣷⡶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⢸⢻⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣀⣀⣀⣀⣀⣠⣤⠶⠛⠁⢀⣾⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣻⣿⣿⣿⣿⣿⣿⣎⣿⡅⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡷⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠻⢿⣿⣿⣟⣂⣀⣀⣀⣀⣀⣀⣤⠴⠋⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣷⡄⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣤⣤⣤⣤⣄⣤⣤⡤⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣦⣤⣤⡀⠀⠀⣶⠀ ⢸⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⠟⢻⣿⣿⡟⠛⠛⠛⠉⠙⠛⠋⠀⠈⠉⠀⠈⠉⠁ ⢸⣿⠿⠟⠋⠉⠀⢀⣾⡿⠉⠀⠈⠸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠹⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
░░░░░░███████ ]▄▄▄▄▄▄▄▄ ▂▄▅█████████▅▄▃▂ [███████████████████]. ◥⊙▲⊙▲⊙▲⊙▲⊙▲⊙▲⊙◤..
⠀⠀⣀⠠⠤⠼⣏⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣞⣴⣿⣿⣷⣮⠻⡶⢵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⢾⣿⣿⣿⣿⣿⡇⡇⠀⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢎⡿⣿⣿⣿⠟⠐⠻⢦⣄⡀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣷⣶⣷⣿⣿⣶⣤⡈⠙⠷⣦⣀⠀⠈⠑⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠷⢮⣝⣻⣿⣿⣷⣦⣄⡙⠻⢶⣤⡀⠈⠛⢷⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣋⣿⣿⣿⣷⣦⣌⡙⣳⣦⣼⣧⠈⣷⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⣿⣿⣿⣿⣿⣿⣇⣠⣯⢹⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣶⣽⣿⡻⣿⡿⠻⣦⢽⠎⢆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⣿⣷⣶⡟⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡉⣧⣼⣿⣁⣸⡗⢀⡞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⠻⢿⣤⣤⡥⠔⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣗⣀⠀⠀⢉⡀⢶⠻⣄⠤⣄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣻⣿⡿⢿⣿⣶⣼⢀⡌⡴⠁⠀⠉⢷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⣿⣿⣿⣿⠟⠉⠉⣩⠷⣿⠀⠻⢲⣀⠎ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢀⣰⣯⣿⣿⣿⣀⣀⣘⣽⣀⣿⣦⣴⠞⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠻⠿⠿⠿⠿⠟⠛⠛⢻⣿⠛⠻⠿⠯⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⢀⣀⡀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⢸⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⠛⠛⠛⠛⠛⠛⠛⣿⡟⠒⠒⠒⠒⠒⢺⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⢻⡃⠀⠀⠀⠀⣀⣿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡆⠒⠒⠒⠚⠛⠛⠛⠛⠛⠻⡏⠫⣌⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⡠⠖⠿⠿⠿⠿⠟⠛⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⣀⣤⣤⣤⣴⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄ ⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋ ⠀⠀⠀⢀⣴⣿⣿⣿⣿⢿⠟⠛⡟⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⠀ ⠀⣠⣴⣿⣿⡿⠛⠉⠉⠣⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣶⣶⣶⣶⣶⣶⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⣀⣀⡈⠉⠙⢇⡀⢀⣈⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢔⣺⣩⣽⣿⣦⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⠞⠓⠿⣿⢸⣤⣽⣇⠻⣛⠉⠉⠈⠳⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡜⡔⣹⠷⠶⢤⢇⡧⠴⠾⢿⣷⣌⠳⢄⠀⠀⠈⠣⡀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⡾⣼⣟⣡⡄⣠⢎⠞⠀⢠⠀⢠⣌⣻⣷⣌⠳⡄⠀⠀⠘⣆⠀⠀ ⠀⠀⢀⡴⠋⠀⡇⣿⣛⡻⢟⣡⠿⠶⠶⠾⢷⣾⠟⠉⠙⢿⣧⡘⣆⠀⣠⣿⣦⠀ ⠀⢀⣏⠀⠀⣴⠟⠒⠐⢒⣿⡏⠀⠀⠀⠀⠈⣿⡇⠀⠀⠈⢿⣷⡈⢿⣿⣿⣿⡄ ⠀⡞⠻⣷⣼⣏⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⢘⣿⣷⠸⣿⣿⣿⡇ ⢸⠃⠀⢨⣿⠛⠿⣶⣶⣿⣿⣤⣤⣤⣤⣤⣤⣼⣿⣶⣶⠾⢟⣿⡟⡇⣿⣿⣿⡇ ⢸⠀⠀⢸⣿⠀⠀⠀⠀⣿⡏⠉⠉⠉⠉⠉⠉⢹⣿⡇⠀⢠⣿⣿⡇⡇⣿⣿⣿⡇ ⠘⣆⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠁⢠⣿⣿⣿⣷⡇⣿⣿⣿⠃ ⠀⢿⠿⣶⣿⣄⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⢸⣿⢰⣿⣿⣿⣿⣿⢰⣿⣿⡟⠀ ⠀⠈⢧⠈⠹⣿⠿⠷⣶⣿⣿⣦⣤⣤⣴⣶⣶⣾⣿⡿⠿⣟⣿⣿⡇⣾⣿⡿⠁⠀ ⠀⠀⠈⢷⣄⠹⣆⠀⠀⠘⣿⡏⠉⠉⠉⣩⣽⣿⠇⣾⣿⣿⣿⣿⣼⣿⡿⠁⠀⠀ ⠀⠀⠀⠀⠹⡟⠿⣦⣀⣀⢹⣷⢠⣴⣾⣿⣿⣿⣼⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠢⡙⣯⢿⣿⣿⡟⣛⣛⣻⣿⡟⣭⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣷⣿⣿⣿⣿⣿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⢀⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⠑⢌⢢⢔⠗⢁⣽⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡈⢳⢔⠕⠁⣠⡏⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢜⠕⠁⠀⠀⠫⠯⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠚⣳⠁⠀⠀⡠⡄⠀⠀⠈⣖⠑⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⢺⣤⠞⢁⠔⢠⡎⣴⣮⢢⡈⠢⡘⠷⡤⠓⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⢊⣴⣇⠀⠔⢁⡔⠓⢻⡌⢡⡟⠛⠂⣄⠀⠀⠨⣦⡑⢤⣀⠀⠀ ⠀⡾⠫⠺⡿⡿⢋⠀⢰⣟⠣⣀⡬⠓⠚⢧⣀⠜⢹⡆⡀⡑⢌⣿⡖⠝⢿⠀ ⢰⣁⡀⠠⠿⡎⠠⠄⢁⠉⣿⣪⠃⠀⠀⠐⣽⢿⢭⡼⠠⡄⢱⡽⠄⢀⣈⡦ ⠀⠀⠨⣄⠎⠐⡀⠀⠀⢡⣧⢻⣄⠀⣀⣰⡏⣼⡔⠀⠀⠀⠆⠘⢤⢇⠀⠀ ⠀⠚⠒⠉⠉⠳⡱⠀⠀⠀⠹⢯⢩⠱⠮⣩⡜⡸⠀⠀⠀⣼⠞⠉⠉⠒⠚⠁ ⠀⠀⠀⠀⠀⠀⢳⢃⠀⠀⠀⢡⠹⡢⠖⡞⠰⠁⠀⠀⠰⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣏⡄⠀⣄⢀⣷⡇⠸⣶⣅⠠⠄⢀⢳⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣞⣤⣴⡿⠋⠀⠀⠘⢿⣷⣤⣨⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⠀⢀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣆ ⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃ ⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⠏⢻⠟⠉⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⡿⠛⠛⢄⡈⢢⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠗⣼⣤⣬⣴⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣾⠟⠉⠁⣀⣀⠀⠀⡙⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣇⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⢠⡶⡿⠿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⢤⣤⣤⣀⣰⢚⣧⣻⣄⠀⠀⠈⠻⣖⢄⡀⠀⠀⠀⢀⣠⣶⣾⣿⢿⣿⣿⣶⣤⣀⠀⠀ ⠀⠀⠀⢀⣠⢶⣫⣭⠶⠛⡷⠞⠉⠉⠉⠉⠉⢙⣿⠷⠾⣿⣿⡏⢿⣷⢀⠀⠀⠙⢷⣝⠀⣠⣾⡿⢋⣵⡶⠿⠿⠿⢿⣿⣝⢿⣷⡀ ⣀⡴⣾⡿⠟⠉⠁⠀⢠⡾⠋⠳⣄⠀⠀⣠⡶⠋⠁⠀⠀⣰⣿⣧⢸⡟⣿⡆⠀⠀⠀⠙⣾⣿⡏⣴⡟⢁⣴⣶⣾⣿⣶⣝⢿⣷⠉⠃ ⣽⣟⣡⣶⡀⠀⠀⠀⣿⣀⣀⣠⣿⡷⠞⠉⠀⠀⠀⠀⣾⣿⣿⣿⣿⣧⠈⢷⣦⡀⠀⠀⢹⣿⠀⡏⢠⣿⣿⣿⣿⣿⣿⣿⣦⠋⠀⠀ ⣵⠋⢹⣿⠀⠀⠀⠀⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣏⢿⡇⠀⠀⢸⣿⠀⣧⡘⣿⣿⣿⣿⣿⣿⣿⠟⣠⠀⠀ ⣀⣠⣾⣿⠀⠀⠀⠀⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣧⣿⠿⣷⣄⠀⠀⣿⣇⠙⢷⣌⠙⠛⠛⠛⣛⣧⡾⠃⠀⠀ ⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠙⠻⣄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠟⠋⠁⠀⠀⠈⠻⣦⠀⠈⢻⡄⠀⠈⠙⠛⠛⠛⠋⠉⠀⠀⣀⡄ ⣿⣿⡟⠀⠀⠀⠀⠀⢀⣠⣾⠃⠈⢧⡀⠀⠀⠀⠀⠀⢠⣻⣿⠁⠀⠀⠀⠀⠀⠀⢰⣿⣷⡀⠀⢿⡄⠀⠀⣀⣠⣶⣶⣤⣀⠀⣿⡇ ⠛⠉⣅⠀⠀⣀⣤⣶⡿⠟⠁⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⢸⡇⣿⣷⣄⠈⣷⡞⢸⣿⣿⣿⣿⣯⢻⣯⣿⣇ ⠀⠈⠛⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⣠⠞⠀⠀⠀⠀⠙⠛⠛⠋⠉⠙⣷⡸⣝⢿⣆⢻⣿⡘⠿⣿⣿⠟⣣⣾⠿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡶⢾⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣯⣽⣦⣝⡻⠷⠶⠶⠟⣋⢰⣿⣿⡿ ⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠛⠚⠛⠉⠉⠈⣿⣿⠁ ⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀
⠀⠀⢀⣀⡀⠀⠀⣤⣤⣤⣾⣿⣿⣿⣷⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣶⣶⠀⠀⣶⣶⡆⠀⢰⣶⣦⠀ ⠀⢰⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣶⣿⣿⣿⡇ ⠀⠀⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⢴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀ ⠀⠈⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⡿⠿⠿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠸⠀⠀⠀⠈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣤⣄⣴⣶⣿⣿⣶⣶⣦⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣶⣀⣶⣆⣶⣦ ⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⠛⢿⣿⣿⣿⣿⣿⠛⡟⠛⢿⡿⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⣿⣿⣿⣿⣧⣀⣀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠙⠛⠿⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣶⣶⣆⣀⢙⣳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣦⣤⣬⣭⣿⣿⣿⣿⣬⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢀⠜⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀ ⢸⣿⣶⡶⠿⢿⣿⣿⣷⣶⣿⣿⡟⠛⠛⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⢿⡿⢿⣿⣿⣿⣿⠿⣿⢿⠿⠛⠇⠈⠛⠋⠉⠁⠈⠉⠉⠁⠈⠉⠉⠉⠀ ⢸⣿⡇⠁⠈⠉⣠⣾⡿⠋⠉⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿⡿⠛⢿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⡇⢀⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠆⠃⠀⠠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣯⠑⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠟⠓⠉⠉⠉⠒⢤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⣠⠖⠉⠉⠉⠓⢤⠙⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢁⠇⠀⡾⠁⡴⣮⣽⣽⡢⡀⢣⠘⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣠⣾⠀⠀⡇⢸⢸⣿⣿⣿⣷⢱⢸⠀⢱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⣀⣴⣿⣿⣿⡀⠀⢷⡈⢮⡻⠿⢿⡣⠃⢸⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⢁⣤⣾⣿⠋⠁⠘⢿⣇⠀⠘⣧⠀⠈⠉⠉⠀⠀⢸⣀⡼ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣊⣠⢞⡽⠛⠋⠉⠀⠀⠀⠀⣿⣦⣀⠸⣆⠀⠀⠀⠀⠀⢸⣿⠀ ⠀⠀⠀⠀⠀⠀⣀⠔⣉⣴⡟⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⢛⣉⣭⣦⢹⡄⠀⠀⠀⠀⢘⣿⠀ ⠀⠀⠀⢀⣴⣾⣷⡿⠟⠉⠀⠀⠀⠀⠀⢠⣾⣿⣥⣶⠾⠛⠉⠀⠈⣆⢻⡀⠀⠀⠀⣸⡟⠀ ⠀⣠⣾⣿⠿⢿⡏⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠉⢹⢿⣄⣤⣴⣾⡟⣋⣮⡛⠶⠶⣖⡿⠃⠀ ⢼⣿⡏⣿⣶⣿⣿⠀⣀⡤⠔⠚⠉⠀⠀⠀⠀⠀⠈⡌⣿⣿⣿⡿⢿⣿⣾⠿⠛⠋⠁⠀⠀⠀ ⠘⣿⣇⢹⣿⣿⣿⠛⣿⣦⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣝⡿⣶⡿⠿⣫⠎⠀⠀⠀⠀⠀⠀⠀ ⢠⣽⣿⡿⠛⠋⠹⠀⢸⣿⡆⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣟⠛⢿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⢿⣿⣤⣰⣦⣴⣧⣀⣿⣥⣴⣶⡶⠾⢿⣿⣿⣿⡿⠖⠮⣿⡀⠷⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢹⣿⣿⣿⣿⢿⣿⣿⣴⣿⣆⠈⠙⢦⡀⣿⣿⡿⢿⠀⣠⣿⣷⣦⣄⠉⣷⠀⠀⠀⠀⠀⠀ ⣰⠃⣾⣿⣿⣿⣦⣿⣿⣿⣿⣮⣓⣄⣀⣷⣏⣿⣷⣼⠛⠋⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀ ⠙⣷⢼⣿⣿⣿⣿⣟⣛⠛⣛⣿⣿⣿⠋⠉⣿⣼⣿⣿⠿⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣶⣿⢟⣿⣿⣿⣛⠿⠿⣿⣿⣿⣿⣾⣿⣟⣿⠟⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢾⡉⠉⣸⣿⣿⣿⣿⣿⣶⣶⣶⣦⣽⡿⠛⠙⢿⡿⠀⠀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⢻⣿⣿⡿⣽⡿⢿⣿⣿⢿⣿⣿⣷⣼⣄⣀⣠⠶⠋⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢾⣿⣷⣿⣿⣿⣿⣮⣝⠻⣾⣭⣿⣿⣽⠟⢁⣆⡤⠶⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠓⢤⣨⣿⣿⡿⠿⣿⣿⣿⣦⣤⣾⣿⠆⣾⠋⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⢿⣾⣧⣾⣷⣦⣭⣛⠻⠭⠿⠥⢾⣧⣀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠒⠢⠬⢉⣛⣛⠛⠛⠛⠒⠒⠒⣛⣻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣠⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢶⠞⠗⠛⠉⠓⢿⣦⡀ ⠀⠰⡀⢄⣀⣼⣰⣀⣠⡤⡆⠀⠀⠀⠀⣨⡟⠉⠀⠀⠀⠀⠀⠈⢧⡇ ⠀⠀⢹⣮⣻⡟⠻⣟⣥⣾⣤⣴⡖⣦⢼⡵⠃⠀⠀⠀⠀⠀⠀⣰⢺⠆ ⠰⢦⣿⣿⣿⣿⣳⣾⣿⣟⡓⠮⠉⠁⠀⠀⠀⠀⢀⣀⣠⡴⢶⡟⠋⠀ ⠀⠀⢸⢟⣿⣿⣿⣿⠿⣏⠀⠀⠀⠠⡤⣀⡠⡴⠯⠟⠉⠉⠉⠀⠀⠀ ⠀⠠⠵⠛⠙⢛⡿⠋⠑⠨⠆⠀⠀⢀⣝⠷⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⢀⣴⣫⡶⠋⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⢴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢔⣵⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣖⣵⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⠀⣤⣤⣤⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣶⣿⡋⢉⣿⣿⠽⣿⣗⡉⢹⣻⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⣿⣶⠿⢿⠷⠟⠛⠁⠀⠈⠙⠻⢾⠿⣿⣤⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣁⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⢻⣧ ⠀⠀⠐⣶⢤⣀⡀⠀⠀⠀⢀⣿⠀⢾⡀⠀⠀⠀⢀⣀⡤⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣘⣿ ⠀⠀⠀⢹⣴⡀⠹⣷⣤⣾⣿⣿⣧⣾⣿⣷⣤⢼⡿⠛⢡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠟ ⠀⠀⠀⠀⠱⣽⣦⣈⣿⣻⣿⡿⢿⣿⣿⡟⣷⡋⢠⣶⣏⣀⡀⠀⣠⣤⣤⣤⣤⡀⣰⣿⣁⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣷⡀ ⠀⠀⠀⠀⢠⣿⣿⣛⣵⣿⣿⣄⠀⠈⠻⣿⣮⣟⣿⣿⡫⢿⣿⢾⣿⣿⣉⣛⣿⣿⠛⠿⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⢹⣿⠁ ⠀⣀⡤⠤⢾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣸⣿⣿⣿⢿⣿⣿⣧⣀⠉⠉⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣸⣿⣿⡿⠃⠀ ⠙⠿⢶⣶⣶⣧⣿⣿⣿⣿⣿⣿⣦⣉⣻⣿⣿⣿⣿⣸⣄⣀⡩⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣰⣿⣟⠛⠻⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠋⣿⣿⠋⠻⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⡟⠻⣮⣿⣿⣿⣿⣿⣿⣟⣴⠛⢯⣯⡀⠀⠀⠀⠀⠀⠀⠀⠐⣶⠦⣄⡀⣀⣠⣶⣦⣼⣿⣿⡾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠎⠁⣠⢞⣽⣿⣿⣟⣛⣻⣿⣿⣿⣦⡀⠱⣿⡄⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⣽⠉⠻⣧⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣰⠿⠚⠉⠀⠉⠙⡏⢸⣿⠛⠉⠀⠈⠳⠦⣍⣷⡀⠀⠀⠀⠀⠀⠀⠀⣾⡉⢿⣯⣷⣈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢻⣸⡟⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠⡾⠛⢻⣦⣀⣿⡄⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⣼⣷⡾⠏⠉⠈⠛⠲⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣫⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣫⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣫⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣯⣾⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⣫⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⣩⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⣩⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⣡⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⣡⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀ ⢸⣻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣿ ⠀⠀⠹⣿⣷⣄⠀⠀⠀⠀⣿⣷⠖⠐⢦⣿⠇⠀⠀⠀⢀⣴⣿⡟⠁⠀ ⠀⠀⠀⠈⠻⣿⣷⣄⢀⣴⡿⠛⠁⠀⠙⠻⣷⣄⢀⣴⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⣿⡟⢏⠀⠀⠀⠀⠀⠀⢀⠿⣿⣿⠛⠀⠀⠀⠀⠀ ⠀⠀⣤⣀⣠⣶⠟⠫⡉⢦⠀⡀⠀⠀⠀⡠⢠⠞⡩⠛⢷⣠⣀⣠⡀⠀ ⠀⠀⢹⠿⠏⠁⠀⠀⠈⢄⠲⣌⠢⡠⢊⡴⢋⠌⠀⠀⠀⠉⠿⢿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⢟⠰⢋⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣡⠊⣐⠃⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠜⡡⠂⠈⠠⡙⢤⡢⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠈⠀⡠⠊⠀⠀⠀⠀⠈⠢⡁⢌⢂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡔⠁⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠑⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠊⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⡊⢂⠀⠀⠀ ⠀⠀⢰⠡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢵⠀⠀
⠀⡠⣐⣚⣯⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⢿⣿⣿⡷⡇⠁⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢿⣻⣥⣍⡓⠦⣀⠁⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠑⢺⣽⣿⣷⣮⣝⡲⢤⡉⢳⢠⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠙⢻⣿⣷⣿⣿⣠⡿⣦⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣽⣏⣱⠘⢡⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣯⣧⡿⠼⢂⠎⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡈⠙⡋⡾⡄⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣾⣿⡿⠻⣕⡖⢥⡀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣼⣿⣿⣀⣘⣧⣷⡴⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⡁⣉⡉⠉⠀⠀⠟⠈⠉⢱⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡊⠉⠉⠉⠉⣿⠉⠁⠀⣙⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢱⠐⠒⠒⠒⠚⠒⠒⢪⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⡠⠴⠶⠶⠿⠁⠀⠀
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢄⣀⠀⢀⣎⣧⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣮⡿⡿⣍⠉⠛⢯⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣤⡏⢀⡛⠋⠸⣏⡟⣷⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠒⣷⠯⠽⢠⠴⡎⢀⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣏⡷⢦⣤⣵⠷⣯⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠁⠀⠀⢧⠇⠀⠈⠻⣮⡹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠻⣮⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡹⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⡻⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡻⣦⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡏⠈⡷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⡀⠀⠀⠀⣠⣶⣶⠶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠧⣄⠙⢷⣟⠀⠀⢈⣷⣿⣁⡴⠋⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣧⣄⠀⠘⠳⣄⠙⢧⣤⠟⢁⡿⠋⠀⢀⣠⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡟⠁⠙⠿⣧⡄⠀⢈⣷⠟⢁⡴⠋⠀⠀⣴⡿⠋⠀⠟⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⢹⣿⡴⠟⢁⡴⠋⠀⠀⢀⣾⡟⠀⠀⢀⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡴⠋⢀⡴⠉⠀⠀⠀⠀⣾⡏⡇⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡴⠋⠀⠀⠀⠀⢀⠔⢳⣑⣽⡋⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠙⢦⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⢦⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠀⠀⠀⠀⠀⠙⢦⣠⠟⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⢀⣴⠻⣦⡀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠁⠀⢀⣴⣿⠏⠀⢀⡴⠂⠀⢀⡴⠋⢠⣤⠎⣿⣦⡀⠀⠘⢦⡀⠀⢻⣷⣄⠀⠀⠈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣈⣷⣴⡿⠟⠁⢀⡴⠋⠀⢀⣴⣟⠀⣷⠶⣿⢶⡏⢈⣿⣦⡀⠀⠙⢦⡀⠙⠿⣿⣦⠞⡃⠉⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣠⡞⠉⠃⠀⠀⢀⡴⠋⠀⢀⣤⣟⣁⡹⣷⡄⠘⠛⠂⢠⡿⢛⣻⣿⣤⡀⠀⠘⢦⡀⠀⠀⠀⠈⢲⡄⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡾⠋⣠⣾⣿⣿⡆⠀⢀⡴⠋⠀⠀⣠⡞⠉⠉⠉⠉⢻⣿⡄⠀⢀⡿⡵⠋⠉⠉⠉⠛⣦⡀⠀⠙⢦⡀⠀⢀⣼⣿⣷⣄⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⣶⠞⢻⣦⣾⣿⢯⣿⡾⣿⡴⠋⠀⠀⣤⣼⡿⡇⠀⠀⠀⠀⢸⠫⠃⠀⠸⡇⡇⠀⠀⠀⠀⢰⢿⣷⡄⠀⠀⠙⠦⣼⠁⠉⣹⣿⣷⣄⡈⠛⣿⣷⣦⡄⠀⠀ ⠀⢻⣽⠟⠁⣶⠟⡿⡏⣯⣏⣾⡿⠋⠀⠀⠀⢰⣿⣿⠃⠹⢦⣀⠀⢠⣯⠶⠚⠛⠓⠿⡿⣆⢀⣀⡤⠏⠀⣸⣿⡇⢀⣀⠀⠈⠳⣄⠹⡾⣿⣿⠷⣶⠊⠙⣦⡇⠀⠀ ⠀⢸⡇⠀⠚⠁⠀⢹⡽⣸⡾⢋⡤⠞⠋⠉⢳⡜⢿⣿⣷⣤⣤⠼⢟⢟⠁⠀⠀⠀⠀⠀⢙⢯⡻⢷⣤⣤⣴⣿⠿⠃⡼⠉⠙⠓⠤⣈⠳⣿⣹⡽⠀⠀⠑⠀⠘⣆⠀⠀ ⣠⡟⠀⠀⠀⠀⠀⣀⣿⣯⣴⠋⠀⢀⣀⠀⠀⢻⢀⡤⠭⢿⣧⡜⢁⡞⠀⠀⠀⠀⠀⠀⠘⢧⡈⣷⢼⣿⢉⣤⣤⣸⠃⠀⣤⣤⠀⠈⢻⣌⡻⣇⠀⠀⠀⠀⠀⠙⢦⡀ ⢿⣶⡶⠶⢦⡄⠀⠉⠙⣨⠿⡀⠀⠘⠛⠀⠀⠘⢾⡒⠃⣸⠋⣇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡼⠀⣿⡈⠙⣺⡞⠀⠀⠛⠋⠀⢀⡏⢧⠙⠋⠃⢀⡴⠒⠚⠿⠿⠃ ⠀⠀⠀⠀⠀⣻⠀⠘⡷⠃⠀⢻⡀⠀⠀⠀⠀⠀⠀⢳⡀⣿⡄⢻⣷⣠⠀⠀⠀⠀⠀⠀⠀⣤⣿⡇⢀⣿⡇⢰⠋⠀⠀⠀⠀⠀⠀⣾⠀⠈⢻⡁⢀⣼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠛⢧⣜⣁⡀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠈⢷⣿⣷⣸⣿⣷⣤⣀⣀⠠⢄⣤⣶⣾⣿⡃⣼⣿⣣⠇⠀⠀⠀⠀⠀⠀⢰⠃⠀⢀⣀⣙⠾⠟⢧⣀⠀⠀⠀⠀ ⠀⢤⣴⣊⣁⡴⠾⠛⠛⠛⢷⣄⠘⣆⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡏⠛⠛⠛⢀⣶⣆⠛⠛⠛⠉⣹⠁⣯⠏⠀⠀⠀⠀⠀⠀⢠⡇⣠⡾⠛⠛⠛⠻⠦⢤⣈⣉⡿⠗⠀ ⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠻⣆⠹⡄⠀⠀⠀⠀⠀⠀⠀⢿⠟⢳⡦⣶⣀⢸⡿⠿⠀⣶⡖⣾⠃⢀⠏⠀⠀⠀⠀⠀⠀⠀⡾⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⢳⡀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠳⣼⡉⠀⢀⢀⠀⢉⡷⠁⢀⡟⠀⠀⠀⠀⠀⠀⠀⣸⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡈⢧⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠹⣟⠺⠾⠿⠛⡟⠁⢀⡞⠀⠀⠀⠀⠀⠀⠀⢠⡇⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠘⡆⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⢘⣆⠀⢀⡾⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⡟⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⢹⡄⠀⠀⠀⣀⡀⠀⠀⣼⣻⣵⡿⠀⠸⣿⣿⣟⢇⠀⠀⣠⣄⠀⠀⠀⣸⢁⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⢳⠀⠀⠀⠛⠃⢠⣼⣽⣿⡿⠁⠀⠀⠙⢿⣿⣮⡳⣄⠉⠁⠀⠀⢰⠇⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡾⠷⢤⣤⣤⣶⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⠻⣿⣿⣾⡗⣤⣤⡤⠾⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣾⠳⣴⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣏⡛⡶⠔⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⢄⡰⠤⠚⡠⡄⣖⡄⠈⠉⠐⠢⢄⠀⠀⠀⠀⠀ ⠀⠀⠉⠦⡸⣅⠼⠓⣉⠭⠭⠅⢒⡠⢄⡈⠢⡀⠀⠀ ⠀⠀⠀⠇⠉⠃⡔⠃⠀⠀⠀⠀⠀⠀⠉⠚⠴⣌⣂⠀ ⠀⠀⠀⠈⢆⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃ ⠀⠀⠀⠀⠈⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢁⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠇⢰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡝⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢄⢤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⣾⢷⡂⣠⢇⢢⠀ ⢰⡵⢴⢿⡛⠻⠉⠀⢂⡇ ⠰⣣⠀⢠⢗⠀⡗⢆⣬⠃ ⠀⠑⠳⢸⠈⢣⠁⠀⠃⠀ ⠀⠀⠀⠀⠀⠈⠇⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡰⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢟⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡽⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟
⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣶⣦⡤⠤⠤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠ ⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡟⢶⡤⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡻ ⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣷⡀⢿⡀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⢠⠃ ⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣷⡌⢷⡀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⢠⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣆⠳⣀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁⠀⠀⢀⠀⠀⠀⡰⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣷⡽⣷⡄⠘⡄⠀⠀⠀⠀⢀⠠⠂⠁⠀⠀⠀⢀⠴⠊⠀⠀⣠⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣾⢿⡦⠘⡄⢀⠤⠊⠁⠀⠀⠀⢀⣤⠞⠁⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡃⣰⡿⠁⠀⠀⠀⠀⣠⡶⠋⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⠋⠹⣷⠀⠀⢀⣤⡾⠋⠀⠀⢀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠏⠀⠀⠀⠹⣆⣴⡿⠋⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⢀⣴⡿⢋⡠⢤⠤⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⣰⣿⠛⠉⠉⢉⡽⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣆⠀⠀⣠⣾⡟⠁⠀⠀⣰⣯⠷⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠈⠻⣇⣴⡿⠋⠀⠀⡠⢾⣿⣿⣶⡃⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢠⢪⡾⠁⠀⢀⠜⠁⠀⠹⣿⣿⣷⡶⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⡰⣻⠟⠀⠀⢠⠎⠀⠀⠀⠀⠘⢿⣿⣿⣧⠌⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡅⠀⢀⠜⣾⠋⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣤⣄⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⢀⢎⡼⠃⢠⡖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣥⣧⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠎⣾⣁⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡏⢣⣀⡴⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣟⣻⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠙⣿⣿⣏⣹⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠘⣿⣿⣏⣼⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠀⠀⠀⠈⢿⣿⣧⡾⢧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣀⡀⠀⣻⣿⣿⣟⣧⡀⠀⠀ ⠀⠀⠀⠀⢀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠟⠛⠛⣿⣿⠟⠃⠀⠀ ⠀⠀⠀⠀⠾⢿⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡞⣉⡀⠻⣿⣿⣷⣶⡾⠻⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⣧⣿⣿⣿⣦⢹⣿⣿⣷⣶⣦⡈⣏⠉⠙⠻⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⢧⡿⡻⣿⣿⣿⡆⢩⣿⣿⣿⣿⣷⢿⣀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡏⡿⠀⠀⠀⡞⢸⣇⣿⣿⣿⣿⣿⣿⣸⣿⢸⢸⢸⣰⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⢻⣿⡈⣆⣶⠇⣸⣿⠛⢻⡿⣿⠟⢹⡇⣿⣾⣎⡿⡏⡞⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣼⣿⣿⣿⣿⢀⡿⡏⠀⠀⢹⠏⠀⣼⠀⢹⣿⣿⣿⣿⣷⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⡟⣿⣿⣿⣿⡾⠁⡇⡄⣠⡟⠀⠀⣿⠀⠀⢉⣉⠙⠻⣿⠿⠿⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⡘⠿⠿⠟⠁⠀⣿⣿⣿⡇⠀⢸⢃⣤⣾⣿⣿⣿⣦⡘⢧⠀⠀⠀⠈⠉⠻⣆⠀⠀⠀⠀⠀ ⠀⠀⠘⣷⠀⢀⣤⣤⠀⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⠟⢷⡘⣷⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀ ⢰⣶⣦⣼⣤⡞⠁⠸⣇⠹⣿⣿⣿⢿⡟⠉⠛⢿⣿⠟⠁⠀⢸⡇⠘⣧⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀ ⢸⡋⠿⠿⡟⠁⠀⢀⣿⡀⠈⠉⠁⡾⠀⠀⠀⣾⠃⠀⠀⠀⠀⣿⠀⢸⠛⠒⠶⠶⠶⢤⣿⡆⠀⠀ ⢸⡇⠀⢸⠇⠀⠀⣼⠁⠹⣦⠀⢰⡇⠀⠀⢸⠇⠀⠀⠀⠀⠀⡏⠀⡟⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀ ⢸⡇⠀⢸⠀⠀⠀⡇⠀⠀⠹⡆⢸⠀⠀⠀⣼⠀⠀⠀⠀⠀⢸⡇⢰⢧⢠⢤⢠⢠⢄⢾⡏⠀⠀⠀ ⠈⣷⠀⢸⠀⠀⠀⡇⠀⠀⠀⡇⢸⡄⠀⣀⣿⠀⠀⠀⠀⠀⣾⠁⣿⡞⡿⡜⣾⣜⣸⣾⠃⠀⠀⠀ ⠀⣿⠀⢸⠀⠀⠀⣷⠀⠀⠀⣿⢸⣷⣿⣿⣿⠀⠀⠀⠀⣸⠇⢸⣿⢻⣳⣷⣷⣿⣿⡇⠀⠀⠀⠀ ⠀⠹⡇⢸⣰⢠⣦⣸⡄⠀⠀⢸⡇⢿⣿⣿⣿⣆⠀⠀⣸⠏⠀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⠘⣿⣿⣿⡿⣿⠀⠀⠀⢻⠈⠻⣿⣿⣿⣦⠾⠃⠀⠀⢹⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⢹⡆⢿⣿⣿⣿⣿⡆⠀⠀⠘⡇⠀⠀⢉⣭⣥⣶⣤⣤⡀⠀⢻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠈⣷⠘⣿⣿⣿⣿⣷⡀⠀⠀⡿⢀⣴⣿⣿⣿⣿⡟⠉⠻⣦⠀⢻⣿⢿⣯⣞⣟⣽⣦⠀⠀⠀ ⠀⠀⠀⢸⡆⠘⣿⣿⣿⣿⣿⣄⣼⢣⡾⣿⣿⣿⣿⠏⠀⠀⠀⠈⣷⡈⢿⡏⠋⠟⠋⠈⠹⣦⠀⠀ ⠀⠀⠀⠀⢷⡀⠈⠙⠻⠿⠿⠛⠁⣼⠻⠿⠿⡿⡿⠀⠀⠀⠀⠀⠈⣧⠀⢷⣄⣀⣀⡀⠀⠙⣧⠀ ⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⣀⠀⠀⡇⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢸⠀⣸⠉⠉⠉⠉⠙⠛⣻⠁ ⠀⠀⠀⠀⠀⢹⡄⠀⠀⣾⣿⡇⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⡿⠀⠀⠀⠀⠀⢰⡟⠀ ⠀⠀⠀⠀⠀⠀⢿⡄⠀⣿⣿⣷⠀⡇⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢸⣧⡇⠀⠀⠀⠀⠀⣼⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⠀⢹⣿⣿⡆⢻⡀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⢸⣿⢃⣠⠀⠀⡀⣠⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣷⣀⣿⣿⣧⠘⣿⣠⢔⣤⣾⣧⠀⠀⠀⠀⢀⡟⣿⡞⡏⣇⣇⣷⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠿⣆⠘⢿⣿⣿⣿⣿⣧⡀⠀⢠⡿⢡⣯⣿⣿⣿⣿⣼⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡈⠻⢿⣿⣿⣿⣿⡶⠋⠀⢸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠈⠉⠉⠁⠀⠀⢀⣾⣿⣿⣿⡿⠟⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠶⠶⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣧⡿⣦⡀⠀⠀⠀⢸⡦⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣉⡿⣤⡏⠀⠀⢀⣼⣷⣌⠹⣆⠀⠀ ⠀⢀⣦⠀⠀⠀⠈⣿⣧⣼⣿⣷⣶⣿⠟⠁⠘⣆⠘⣇⠀ ⠀⡾⣈⣷⣶⣶⣶⣿⡟⠛⠋⠙⣇⠀⠀⠀⠀⠸⡄⢹⠀ ⢰⡇⡇⠀⠉⠉⠉⠸⣿⡄⠀⠀⢹⡀⢀⡀⠀⠀⡇⢸⠀ ⠀⣇⢹⡀⠀⠀⠀⠀⢹⣿⠄⠀⢻⡟⠻⡟⠀⢠⣧⡏⠀ ⠀⠘⣆⢳⡀⠀⠀⣾⣿⠻⣄⠀⠸⣧⠀⠙⢳⣾⡿⠁⠀ ⠀⠀⠈⠳⣿⢦⡄⠀⡿⠀⠹⣗⠚⢻⠀⠀⠀⠛⠁⠀⠀ ⠀⠀⠀⠀⠈⠛⠷⣤⣇⠀⠀⢸⣧⠈⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⢻⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠈⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⢸⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢿⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣻⢿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣾⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡷⣾⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢹⠀ ⠀⠀⠈⢷⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣼⠀ ⠀⠀⠀⠈⢳⠈⠑⠦⣄⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢀⠇⠀ ⠀⠀⠀⠀⠀⢳⡀⠀⠀⠙⡆⠀⡴⠋⠉⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⡼⠀⠀ ⡗⠦⣄⡀⠀⠀⠳⣄⣀⡴⠓⠚⠁⣠⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢠⠀⠀⡼⠁⠀⠀ ⡇⠀⠀⠉⠙⢲⠀⠀⣨⠇⠀⠀⣸⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠁⠀⡠⠁⢀⡞⠁⠀⠀⠀ ⢹⠀⠀⠀⠀⠈⠙⠉⠀⣠⠞⠻⣇⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠀⠀⢀⠜⠀⣠⠋⠀⠀⠀⠀⠀ ⠈⣇⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠈⠳⣄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⡰⠋⢀⠜⠁⠀⠀⠀⠀⠀⠀ ⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠉⡇⠀⠀⠈⠳⣄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⡠⠊⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠈⠢⡀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡠⠊⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠓⠢⠤⢀⣀⣀⡙⣆⠀⠀⠀⠀⠈⠢⡀⠈⠢⡀⠀⠀⠀⠀⠀⢀⠴⢋⠠⠊⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠢⡀⠙⢦⡀⢀⡠⠞⢁⠔⠁⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⢯⡠⠚⢁⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⣹⢦⡀⠙⢶⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⢁⡠⠊⢁⡠⠛⢦⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⡠⠔⠁⣠⠔⠋⠀⠀⠀⠙⢦⡀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⢷⣼⣦⡀⠀⠀⠀⠀⣠⠖⠋⡠⠔⠉⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢏⠳⣄⣠⣴⡯⣧⠔⠉⣀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣨⡇⡤⠁⡶⢰⣇⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡠⠚⣽⠀⠇⠒⠃⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠋⠀⠀⢛⡿⠛⠉⠹⣌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⡴⠋⠀⠀⣠⠞⠁⠀⠀⠀⠀⠈⢳⡉⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠳⣄⠀⠀⠀⠀ ⣸⢁⠤⡄⢸⠃⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠈⠳⡀⠀⠀ ⢹⡘⣦⡇⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠈⢢⡀ ⠀⢙⣛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢰⡿⠈⣿⡄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⣶⣤⣀⢀⣤⣿⣷⣶⣾⣿⣄⡀⢀⣠⣴⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣷⢀⣽⣿⢿⣿⣯⣉⠉⠉⠙⠻⢿⣿⣍⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣿⡟⠁⢸⣏⠈⢻⣷⡄⣀⡀⠀⠙⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣿⡟⠀⠀⢸⣿⠾⠟⠋⠀⣿⡟⠛⢻⣿⣿⣧⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣤⣴⡶⠟⢻⣿⠀⠀⣠⣶⣄⠀⠀⠀⠀⠹⣷⣴⡿⠃⢹⣿⠉⠛⢻⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠛⠿⢶⣦⣼⣿⣤⣾⠟⠉⣿⡆⠀⠀⢀⣀⣈⠋⠀⠀⣼⣿⡶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⢿⣿⡿⠿⠿⠿⠇⢠⣾⠟⠛⣿⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡿⣿⣦⡀⠀⠀⠈⠻⢷⣤⣿⣀⣼⡿⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡟⢀⣩⣿⣿⣷⣶⣤⣤⣬⣿⣿⠿⣿⣦⡀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠛⠋⠁⠀⠈⣿⡍⠉⣿⠏⠁⠀⠈⠻⣿⣦⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠸⣷⣼⡏⠀⠀⠀⠀⠀⠈⠻⣿⣆⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠹⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠈⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠈⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠈⠻⣿⣦⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣾⡿⠿⢿⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡏⠀⠀⠀⢹⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣤⣴⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣄⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣾⣏⣉⣿⠟⢿⣯⣉⣿⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⣿⡟⠙⠛⠉⠁⠀⠀⠈⠉⠛⣿⣶⣄ ⠀⠀⣤⣀⡀⠀⠀⠀⣸⠃⣇⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣁⣿ ⠀⠀⠹⣦⠉⢷⣶⣾⣿⣷⣾⣷⣶⡾⠟⣡⠃⠀⠀⠀⠀⠀⠀⢀⣴⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟ ⠀⠀⠀⢹⣷⣦⣿⣿⡟⠛⢿⣿⡻⣤⣾⣷⣶⣄⣴⣶⠶⣶⣦⣾⣷⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⡇ ⠀⣀⣀⣿⣿⣿⣿⣿⣿⣦⣀⣙⣿⣿⣿⣷⣿⣋⠙⠻⠖⠛⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⣿⣶⡿⠁ ⠛⠷⠶⣾⣿⣿⣿⣿⣿⣯⣹⣿⣿⣿⣿⣯⠭⠝⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣴⣿⡛⣻⣿⠏⠉⠀⠀ ⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⠇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⢰⣿⣍⣽⡿⠈⠙⠛⠉⠁⠀⠀⠀⠀ ⠀⠀⢀⠞⢋⣴⣿⣿⣿⣿⣿⣿⣿⣌⠻⣧⠀⠀⠀⠀⠀⠀⠹⣍⢲⠖⢾⣛⣿⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢼⠴⠟⠋⠉⠙⢟⢹⡟⠋⠉⠙⠢⢬⣧⠀⠀⠀⠀⠀⢀⣟⡹⣯⣇⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣉⣷⠦⠿⣌⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣵⣿⠟⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⣾⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡾⣫⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣴⣶⣶⣤⣤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⣀⣻⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢀⣹⣿⠟⠻⣶⣶⣄⠀⠀⠙⣷⣶⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡷⠞⣋⣽⣇⣴⢾⣿⢿⣿⣷⡄⠀⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢋⣴⣿⣭⣿⣿⣿⠀⣿⠀⠈⣿⣿⠀⢸⣿⠿⠟⠛⠋⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⣿⠁⠀⠀⠉⠉⣿⢠⡟⠛⠛⢿⣿⣧⡀⠙⢶⣄⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢡⡞⢁⣿⡿⠶⢶⣦⣴⠇⣼⣧⣴⡶⠿⢿⣿⣿⣦⣄⠙⠳⣄⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢡⣿⣶⠟⠋⠀⠀⠀⣸⠟⣼⠏⠀⠀⠀⠀⠀⡈⠛⢿⣿⣷⣄⠈⢳⣄⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠃⣿⣿⣧⣠⣾⠃⢀⡼⠋⣼⠋⠀⠀⢰⣦⠀⠀⢻⣦⣀⣿⣿⣿⣷⣄⠙⢷⡄⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⠟⠁⠀⣿⢸⣿⠿⠿⢿⣿⡾⠋⣠⣾⣧⣤⣤⣤⣤⣿⣷⣶⣾⣿⠿⠛⠉⠻⣿⣿⣦⡈⢻⣆⠀⠀⠀⢀⣿⣿⡄⠀⠀ ⠀⠀⢀⣴⠟⠁⠀⠀⢀⣿⡈⠻⠶⠶⠛⢋⣠⣾⡟⠉⠉⠉⠉⠉⠉⠉⠹⣿⣿⡇⠀⠀⠀⠀⠙⣿⣿⣷⡀⠻⣦⣤⣴⣾⣿⣿⣿⡄⠀ ⠀⠀⣾⡏⠀⠀⠀⢀⣾⡿⠛⠶⠶⠶⠛⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⠀⠀⠀⠀⠀⠘⣿⣿⣷⡄⠹⣿⣿⣿⣿⣿⣿⣧⠀ ⠀⣼⣿⣿⣦⡀⢠⣿⡿⠁⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡆⠀⠀⠀⠀⠀⢹⣿⣿⣷⡀⢻⣿⣿⣿⣿⣿⣿⡄ ⢸⡏⠀⠙⢿⣿⣿⣿⣅⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⢀⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⡇ ⣿⠀⠀⠀⠀⣹⣿⣿⣿⣿⣷⣶⣤⣤⣾⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣤⣤⣶⣶⣿⣿⣿⣿⣿⢿⡆⢹⣿⣿⣿⣿⣿⡇ ⣿⠀⠀⠀⠀⣿⣿⡇⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⢉⣴⣾⣿⣿⢸⡇⢸⣿⣿⣿⣿⣿⡇ ⣿⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢹⣿⣿⠃⠀⠀⠀⣼⣿⣿⣿⣿⢸⡇⢸⣿⣿⣿⣿⣿⡇ ⣿⠀⠀⠀⠀⣿⣿⡁⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⣸⣿⣿⣿⣿⣿⢸⡇⢸⣿⣿⣿⣿⣿⠀ ⠹⣧⣀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠃⣼⣿⣿⣿⣿⡏⠀ ⠀⣿⣿⣷⣤⣽⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⠀⠀ ⠀⢻⣧⠙⠻⣿⣿⣿⣦⣄⣀⡀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⠇⣸⣿⣿⣿⣿⠇⠀⠀ ⠀⠀⢻⣧⠀⠀⠙⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣶⣴⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⢠⣿⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠻⣧⡀⠀⠸⣿⡆⠀⠀⠉⠉⠛⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⢛⣿⣿⣿⠉⣥⣶⣶⣿⣿⣿⣿⣿⢃⣾⣿⣿⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣷⣦⡀⠹⣿⡄⠀⠀⠀⠀⠸⣿⣿⡀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣿⢷⣿⣿⣄⠀⠀⠀⠀⢿⣿⣇⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣦⡈⠻⣿⣿⣷⣦⣤⣼⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡘⢿⣏⣭⣽⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⡏⣭⣴⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⣿⣾⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢐⡖⠒⠒⠒⠒⠶⠤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣄⣀⣄⢀⣿⠤⠼⠟⢁⣤⣀⢠⡞⣲⠀⠀⠀⠀⠉⠑⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠓⠮⣉⠁⢠⡶⢦⠘⣷⣿⣤⡿⠿⠦⠤⠤⠤⣄⣀⠀⠀⠈⠑⠦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⡷⣜⠓⣯⠴⠋⠁⣀⣠⠴⠖⠒⠒⠦⠤⢌⣉⠒⠤⣀⠀⠈⠢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠀⠉⠻⣅⣀⡰⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢽⣦⣄⠈⢦⡀⠀⠀ ⠀⠀⠀⠀⠘⢆⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣷⡀⠀ ⠀⠀⠀⠀⠀⠈⢧⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠂ ⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠁⢀⣀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡇⠀⠻⠿⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡙⣧⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⣄⢲⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇ ⠀⠀⠲⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠇ ⠀⠀⠀⠡⡈⠑⢄⠀⡤⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⡸⠀ ⢸⠂⠄⣀⠑⠤⡞⠊⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢃⠆⡠⠁⠀ ⠘⡀⠀⠀⠒⠊⡠⠲⡛⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠠⠂⡔⠁⠀⠀ ⠀⢡⠀⠀⠀⠀⠣⡄⠈⠢⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢃⠔⡠⠊⠀⠀⠀⠀ ⠀⠀⠑⠄⡀⠀⠀⠰⡀⠀⠘⢄⠑⢄⠀⠀⠀⠀⠀⡠⢊⠔⡡⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠐⠒⠒⠀⠀⠀⠑⢄⠑⢄⢀⡠⠊⠔⡡⠊⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⢄⠣⣊⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠔⡉⠗⢌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣲⡀⠀⠀⢀⡠⢊⠅⢊⠄⠊⠀⠀⠀⠑⡈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠕⠤⢶⠱⢊⠠⠊⠁⠀⠀⠀⠀⠀⠀⠈⠢⡈⠢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠔⡏⢧⠆⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⢂⠀⠀⠀⠀⠀ ⠀⢠⠞⠁⡠⠛⠁⠈⢼⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡑⢄⠀⠀⠀ ⢀⢣⠀⠘⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠑⢄⠀ ⠀⢫⠷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠃
⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢿⣿⣿⣿⣿⡭⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴ ⠀⠀⠀⠻⣿⣿⣿⣧⡹⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠊⠀⡌ ⠀⠀⠀⠀⠈⢻⣿⣿⣷⡕⣄⠐⡀⠀⠀⠀⠀⡀⠄⠒⠉⡀⠀⢀⠊⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣯⣧⡠⡀⡠⠐⠈⠀⢀⠔⠈⢀⠔⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠴⡏⠀⠀⡠⠊⠁⢀⠔⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠁⠀⢳⡴⠋⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⣴⠟⠒⡺⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⠺⣄⣠⡾⠁⢀⣴⣟⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠁⠀⣼⠏⠀⡐⠁⠹⣿⣶⡐⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠁⢀⣮⠋⢀⠌⠀⠀⠀⠘⢿⣯⣈⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣡⡳⢁⠎⠁⠀⠀⠀⠀⠀⠀⠻⣿⣾⠄⢀⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡱⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣞⣅⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠈⢿⣖⣣⡀⠀⠀ ⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠈⢿⣷⣣⠀⠀ ⠀⠀⢐⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠚⠻⠿⠃⠀ ⠀⠀⠉⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣄⡲⣦⣤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⠿⣿⣘⣿⣷⣧⡈⠉⢢⠀⠀⠀⠀⠀⠀ ⢸⣷⣤⢣⡟⢻⠟⡟⣿⣷⣽⡀⠀⠀⠀⠀⠀ ⠘⣿⣿⠎⣧⡜⢠⢃⣭⣝⢟⠃⠤⢄⠀⠀⠀ ⣀⣡⡠⢢⢿⣧⡾⠻⣿⠟⢋⢆⠀⠀⢇⠀⠀ ⡏⢹⠁⡘⢢⢀⠃⢰⠁⠀⢸⠸⠉⠁⢘⠇⠀ ⢣⢈⠀⡇⠀⣾⢀⡄⠀⠀⡌⣷⣶⣞⡟⠀⠀ ⠸⢸⣴⣥⠀⢫⢿⣿⡀⡔⢸⣿⣿⣿⠃⠀⠀ ⠀⠏⣿⣿⡆⠈⡌⣩⣷⡦⢄⢻⣿⣿⣆⠀⠀ ⠀⠸⡘⠿⠿⠖⣼⡿⡟⠀⠈⢆⢫⠉⠉⢢⠀ ⠀⠀⢣⠀⣤⡄⠁⠀⡇⠀⠀⠸⡼⠀⠈⢹⠁ ⠀⠀⠈⢆⢻⡇⡆⠀⢃⠀⠀⢰⣇⠀⣀⡎⠀ ⠀⠀⠀⠈⠚⠛⡜⢿⣿⣦⣀⢊⣿⣾⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠈⠢⢍⣉⣁⠼⠿⠟⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣍⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣤⠬⠷⠶⠤⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠋⠁⠀⣀⣀⣀⣀⣀⠉⠳⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⠃⠀⣀⡴⠋⠁⠀⠀⠀⠈⠳⣆⠘⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⢰⠇⠀⣰⠟⠀⣠⢖⣫⣭⣝⠲⣄⠈⢧⠈⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⢀⡏⠀⠀⣿⠀⢸⢡⣿⣿⣿⣿⣷⡸⡀⢸⠀⢸⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⣠⣶⣿⡇⠀⠀⢿⡀⢸⠸⣿⣿⣿⣿⣿⢣⠇⢸⠀⠀⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣀⣴⣿⣿⣿⣿⣷⠀⠀⠸⣷⠈⠳⣍⡛⠿⣛⣡⠎⠀⢸⠀⠀⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣀⣤⣾⣿⣿⠋⠁⠈⢿⣿⡇⠀⠀⢻⣇⠀⠀⠉⠉⠁⠀⠀⠀⢸⠀⣠⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⢁⣤⠾⣻⡿⠿⠿⠃⠀⠀⠀⠀⠘⣿⡀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣷⡶⠛⠑⠚⠁⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⡷⢦⠘⣷⡀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⢋⣤⢾⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠿⠟⢋⣉⣤⣶⡿⢧⠹⣧⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀ ⠀⠀⠀⠀⠀⣀⣴⣿⣧⣾⣫⠖⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣏⣤⣶⣾⠿⠛⠉⠀⠀⠘⣆⢹⣇⠀⠀⠀⠀⠀⣸⣿⠀⠀ ⠀⠀⢀⣠⣞⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠿⠛⠋⣿⣿⣇⠀⢀⣀⣤⣴⡿⠟⣆⠻⢷⣤⣄⣠⡴⣻⠏⠀⠀ ⢀⣔⣿⣿⣿⣏⣡⣩⣿⡄⠀⠀⠀⠀⢀⣠⡴⠖⠛⠉⠀⠀⠀⠀⢻⡘⣿⣾⣿⣿⣿⣿⣶⢖⣋⣷⣦⣬⣭⠽⠞⠋⠀⠀⠀ ⠸⣿⣿⡆⢹⣿⣾⡿⣿⣇⢀⣤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢹⣝⠿⣿⡿⠟⣛⣯⣽⡷⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⣿⣇⠀⣿⣿⡿⣿⡿⠙⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣧⡙⠿⣷⣿⡿⠿⣫⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⣿⣿⣿⠿⠟⠛⡇⠀⢻⣿⣧⠀⠀⠀⠀⠀⣀⣴⣾⢿⣿⣿⣿⣿⣿⠿⠷⢶⡒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⠛⠁⣀⡀⠀⣹⡄⠈⣿⡿⠀⠀⣀⣀⣘⡿⣿⣷⣿⣿⣿⣿⣛⣛⠷⣦⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⣟⣟⡻⣷⣦⣿⣿⣾⣿⣷⣤⣿⢷⡶⠿⣿⣿⡛⠛⠺⢯⣿⢹⣿⣿⡋⠉⠳⣽⣇⠀⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⢹⣷⣽⣿⡿⠿⣻⣭⣷⣶⣿⡿⣄⠀⠈⠻⣧⡀⢸⣿⣿⡏⣯⡇⠀⣠⣯⣿⣷⣦⣤⡀⢈⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⠋⣴⣟⣽⣷⣿⣆⣹⣿⣿⣿⣿⣷⣙⢧⣄⠀⠈⣷⣸⢺⣏⣧⣀⣶⠿⠛⠻⠿⠿⠿⠯⠵⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣇⣄⠙⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡷⢶⣶⠾⠿⣿⡖⣿⡹⣿⣧⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣏⠛⣿⣿⣿⣿⣿⣗⣦⣤⣀⣤⣴⣶⣶⣿⣧⡀⠀⣿⣿⣼⣿⣿⡙⠃⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⣷⣿⡿⣛⣽⠟⣿⣿⣛⠛⠻⢿⣿⣿⣿⣿⣿⣾⣿⣿⣛⣽⠟⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡟⠛⠉⠉⣾⣿⣾⣿⣿⣿⣿⣷⣶⣶⣷⣮⣉⣽⡿⠿⠏⢻⣿⣿⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠙⢦⡶⣽⣿⣿⣿⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡆⠀⠉⠁⢀⣤⠶⠋⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣯⡿⠿⣛⣻⣿⣟⣛⠿⣯⣝⣛⠿⢿⣿⣿⣾⣧⢤⣤⡾⠋⠁⠀⢀⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣹⣿⣿⣿⣿⣿⣿⣿⣧⣴⣍⠛⡿⣶⣮⣭⣭⣵⡿⠋⢀⡞⣠⠖⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⢤⣄⢙⣿⡿⢿⣿⣟⣿⣿⣿⣿⣦⣬⣭⣽⣿⢿⠀⣾⡞⠁⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⣾⣅⣿⣏⣭⣤⣉⠙⠿⢿⣟⣿⠿⢿⠿⣠⣾⡏⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣇⠻⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⣉⠙⠛⠛⣉⣽⡟⣤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⢤⢤⣉⣛⣛⡛⢛⣛⣛⣛⣛⣛⣛⣛⣥⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⢦⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡟⡷⣱⠂⠀⢀⣧⡝⢦⡀⠀ ⠀⣴⡀⠀⠈⢹⠧⣿⣷⡶⠿⠋⠘⣆⢱⠀ ⢸⢣⠻⠿⢿⠿⣏⠉⠀⢧⠀⠀⠀⠸⡀⡇ ⢸⡸⠀⠀⠀⠀⢿⣆⠀⢼⠤⣲⠄⢀⣷⠃ ⠀⢣⣳⡀⠀⢰⡾⢧⡀⠸⡇⠘⠲⣾⠏⠀ ⠀⠀⠑⢷⣦⠀⡟⠈⢻⡉⢣⠀⠀⠉⠀⠀ ⠀⠀⠀⠀⠈⠑⠓⠀⠀⣿⠈⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠸⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠂⢣⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠈⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣠⣿⠀⠀⠀⠀⠀⣀⠉⠉⠉⠙⠒⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣤⠤⢤⣄⣀⣿⠳⠦⠾⠛⠁⣠⠴⣄⠀⣿⡉⣽⠄⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠙⠛⠦⣬⡉⠁⠀⢠⡤⣤⠀⠻⣤⣟⣇⣼⣿⡿⠤⠤⠤⢤⣄⣀⡀⠀⠀⠀⠀⠉⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣷⡀⢹⣤⣼⢀⣠⠿⠟⠋⠉⠉⣀⣀⣠⣄⣀⣀⡈⠉⠓⠲⢤⣄⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡇⠻⣦⣀⡾⠛⠁⠀⣀⡶⠖⠋⠉⠁⠀⠀⠀⠈⠉⠉⠓⠲⠦⣌⡙⠳⢤⣀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⠁⠀⠈⠻⢶⣄⣀⡾⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠶⢭⣳⢤⡀⠘⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣌⣳⡀⠀ ⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣷⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⢀⣀⣀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢸⣭⣹⠗⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡿⣦⡄⠀⠈⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢷⡘⠻⠀⠀⠀⠀⡾⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠰⣆⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠻⣷⡦⠀⠀⢾⡿⢋⡿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡁⠈⠳⣌⠳⣄⡴⢛⡿⠋⠀⣨⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠈⠻⣦⡀⢈⡷⢋⡴⠋⠀⣠⡾⠋⢙⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⠀⢘⡿⢋⠔⠉⠀⠀⣼⢿⠀⣀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⢁⠔⠁⠀⠀⠀⡰⢿⣸⡖⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢁⠔⠁⠀⠀⠀⠀⠀⢀⠜⠁⠙⢦⡈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠙⣳⠃⠀⠀⠀⠀⠀⣠⡖⠁⠀⠀⠀⠀⠘⡶⠋⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⣴⠟⠀⣠⠀⠀⣀⠜⣁⡩⢦⡀⠀⠠⣄⠀⢻⣦⡀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣩⡷⠶⠟⠁⣠⠞⠁⣠⣾⡁⠶⢾⡷⠏⢸⣦⡀⠈⠳⢄⠙⠿⠦⠞⣉⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⣡⣾⡁⠁⠀⣠⠞⠁⢀⡴⠿⠤⣽⣆⠉⠉⣰⣏⡭⠿⢦⣀⠀⠑⢄⠀⠀⠈⣷⣄⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⣀⣠⡴⢮⣡⣾⣿⣿⣷⡠⠚⠁⢀⣴⣿⠀⠀⠀⢈⣿⠀⠀⣿⡇⠀⠀⠀⣸⣷⡀⠀⠑⢄⡘⠙⢻⣷⣄⠙⢶⣤⣄⡀⠀ ⠀⢺⡽⠋⡴⠻⣿⣻⣿⡿⠋⢁⣀⠀⣿⣟⠈⢦⣀⣀⣼⠖⠒⠒⠻⣷⣀⣀⠴⠁⢹⣿⡆⣀⡀⠙⢦⡘⢿⣿⡗⢦⠙⢧⡇⠀ ⠀⡸⠀⠈⠀⠀⢻⡿⢋⠴⠊⠁⠈⢧⠛⠿⣷⡶⣺⠟⡅⠀⠀⠀⠀⢘⠻⣟⢶⣶⠟⠛⢠⠁⠈⠑⠢⣽⢯⣷⠁⠀⠁⠀⢧⡀ ⢼⣥⣤⣀⡀⠰⠺⢛⣯⠀⠰⠷⠀⠸⣴⠭⢹⡿⣇⠞⠀⠀⠀⠀⠀⠀⢳⣹⠹⡗⠺⣽⡇⠀⠿⠇⠀⣸⡟⠟⠢⠀⣠⠤⣤⡷ ⠀⠀⠀⠀⣱⠀⢰⠎⠈⣆⠀⠀⠀⠀⠈⢧⣸⡇⢻⣇⡀⠀⠀⠀⠀⠀⣼⡇⢸⣿⢠⠋⠀⠀⠀⠀⢠⠃⠘⢎⠀⣼⠀⠀⠀⠀ ⠀⠀⢀⡰⠛⣳⣥⣤⡀⠘⡄⠀⠀⠀⠀⠈⢿⣿⣼⣿⣶⣦⢄⡒⣶⣿⡿⢧⣾⣿⠋⠀⠀⠀⠀⢀⠎⢀⣤⣬⣟⡋⠣⠄⣀⡀ ⠀⠙⠓⠒⠋⠁⠀⠀⠙⣦⠹⡀⠀⠀⠀⠀⠈⢿⡿⣤⣀⠀⣾⣿⡄⣠⢤⡞⢈⠏⠀⠀⠀⠀⠀⡜⣴⠋⠀⠀⠈⠉⠒⠒⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢣⠀⠀⠀⠀⠀⠈⣆⠙⢾⡁⠀⣀⡀⣹⠎⢀⡎⠀⠀⠀⠀⠀⣸⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡎⢇⠀⠀⠀⠀⠀⠘⢆⠈⢏⠛⠛⢹⠃⢀⡞⠀⠀⠀⠀⠀⢠⢃⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡸⡄⠀⠀⠀⠀⠀⠈⣶⣾⡆⠀⣯⣤⣞⠀⠀⠀⠀⠀⠀⡌⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢱⡀⠀⠸⠇⣠⣾⣿⡟⠁⠀⠙⣿⣮⣣⡀⠛⠀⠀⢰⢡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣳⡲⢤⣾⣿⡿⠋⠀⠀⠀⠀⠈⠻⣿⣿⣷⡤⠖⣣⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣙⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣿⣸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⠱⠄⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⠋⡠⠂⣀⠂⠕⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢁⡆⢸⢰⣵⣿⣮⡌⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⢊⣤⡾⢻⡇⠘⡎⠪⠿⠕⠀⠀⡇ ⠀⠀⠀⠀⢀⢤⡪⠲⠛⠛⠀⢀⣹⣤⡸⡀⠀⠀⠀⡎⠀ ⠀⠀⣠⣖⡵⠟⠁⠀⠀⣠⣖⣭⠵⠚⠑⣳⠀⠀⢠⡇⠀ ⣴⢾⣟⣿⠀⠀⡀⠤⠒⠉⠁⣻⣴⣶⣯⣕⣽⠶⠕⠁⠀ ⢻⣏⣿⣿⠺⣇⠀⠀⠀⣀⣠⣵⣻⣿⣞⠟⠀⠀⠀⠀⠀ ⣾⣟⣡⣀⣆⣿⣀⣤⠾⣿⣿⡿⠟⣌⢂⡀⠀⠀⠀⠀⠀ ⡸⣿⣿⣟⣿⣾⡷⡈⠳⣸⣿⢻⡴⠿⣶⣤⠇⠀⠀⠀⠀ ⢳⢽⣿⣿⣟⣛⣿⣯⣋⣹⣽⣗⠖⠄⠀⠀⠀⠀⠀⠀⠀ ⡞⢛⣷⣿⣿⣭⣽⣟⡿⠟⣿⠁⢀⡌⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣟⣿⣟⡻⢿⣻⣷⣧⡤⡊⣁⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢩⡿⡿⡿⢷⣯⣭⡿⣠⠏⠠⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠫⠽⢛⣿⠿⠾⠭⠭⢿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⠀⠀⠀⢰⣿⣿⡇ ⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣭⣤⣄⣠⣄⡀⠀⢈⣷⣶⡾⢻⣯⡀ ⠀⢀⣠⣶⣿⣿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠿⠿⠿⣿⣿⣿⢛⡇⣾⠷⠃ ⣰⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣿⠏⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡎⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡸⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡰⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡸⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡰⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⡀⠀⡜⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⢿⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣹⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡼⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣉⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠰⣦⣄⡀⠀⠀⢠⣿⣈⣿⡄⠀⠀⠀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣏⢙⣷⣾⣿⣟⠛⠛⠻⣶⣾⡛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣹⡿⠋⢸⡏⣻⣷⢀⣀⣀⣙⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣠⣴⣿⠁⠀⣘⠛⠋⠁⠈⣿⣉⣽⠿⣿⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠿⢯⣭⣸⣷⣠⡾⠻⣧⠀⠀⠀⢘⠟⠁⢀⣿⣤⡶⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⢿⣿⠓⠚⠛⢠⣶⠛⢻⠃⢀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠻⣷⣤⣀⠀⠉⢻⣾⣶⣿⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⡷⠶⠛⠉⢻⡟⠛⣿⠟⠉⠻⣷⣄⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢿⣼⠏⠀⠀⠀⠈⠻⣷⣄⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠙⢿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠙⣿⣦⣄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⠉⠉⢻⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⣠⣾⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀
⣠⣶⢶⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣴⣶⡦⡄ ⣿⢿⣫⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣷⣗⢾⡇ ⠛⠛⢿⣷⣷⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠛⠃ ⠀⠀⠀⠙⢿⣿⠭⣧⡄⠀⠀⠀⠀⠀⠀⠀⢻⢷⢹⡾⠓⠀⠚⢶⡿⣻⠇⠀⠀⠀⠀⠀⠀⠀⣠⡾⠽⣿⠟⠃⠀⠀⠀ ⠀⠀⠀⠀⠈⠹⣿⣿⣟⣧⡄⠀⠀⠀⠀⢠⣮⣿⣿⡷⠀⠀⠀⣿⣷⣷⡳⡀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣗⣚⣿⡦⡄⣀⣴⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠺⢿⣿⣦⣀⣠⣾⣿⣒⣺⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣽⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⢿⣯⣽⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡿⢿⣧⡈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⣼⠮⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⣤⢀⣀⢴⣾⡿⠛⠑⢄⠑⢵⣄⠈⢦⡀⠀⠀⠀⠀⠀⢀⡴⠃⣰⡿⠋⣰⠛⠛⢿⣗⢦⣄⡀⣠⣄⠀⠀⠀ ⠀⠀⠸⢿⣾⢍⣾⡟⡿⠀⠀⠀⠈⠳⡀⠱⣕⣄⠑⣄⠀⠀⠀⡠⠋⣠⡪⠋⢀⠞⠁⠀⠀⠀⠻⢻⣖⣫⣿⡿⠃⠀⠀ ⠀⠀⠀⢰⡟⠛⠟⠂⠀⠀⠀⠀⠀⠀⠙⢦⡈⠫⡢⡈⠳⣤⠞⢀⢾⠋⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠿⠋⢺⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠘⢊⠞⢁⣴⠟⠁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⠁⣠⡚⠁⡠⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢠⡾⠋⣠⠞⠥⡀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢁⢔⠋⢀⠞⠉⠢⡀⠫⡢⡈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠔⠗⢁⡴⠋⠀⠀⠀⠙⢆⠈⠳⣄⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⡠⠊⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠑⢄⠉⢧⡀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠜⠁⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠙⢄⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠑⣄⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠢⠈⢧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠋⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠢⠱⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⠁⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠘⢆⠀⠀⠀⠀ ⠀⠀⠀⢸⠵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢾⡆⠀⠀⠀
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⠀⠀⠀⣀⣀⣤⣼⣿⡏⠓⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⢞⣩⣤⣤⣤⣍⡻⣦⣄⡹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⢫⣿⣿⣿⣿⣿⣿⣷⠈⡇⠙⠻⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢺⠸⣿⣿⣿⣿⣿⣿⣿⠃⣷⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢧⡻⣿⣿⣿⣿⣿⠟⠐⠿⣷⣦⣀⠀⠀⠀⠉⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠲⣬⣉⣯⣴⣿⣶⣄⡀⠉⠛⢿⣦⣄⡀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⣿⣯⣛⠿⣿⣿⣿⣿⣶⣤⣀⠉⠻⢷⣦⣄⠀⠀⠈⠳⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠻⢿⣶⣨⣝⣿⣿⣿⣿⣷⣦⣄⡈⠙⠿⣶⣄⡀⠀⠈⢻⣯⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⣏⣴⣿⡿⣿⣿⣷⣦⣄⡉⠻⣷⣦⣸⣿⡆⠘⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣿⢙⢾⣷⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⣿⣍⠻⣿⣿⣿⣾⣿⣿⣿⡈⠛⢮⡻⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣾⣿⣿⣿⢇⡎⣹⣿⡋⠉⣻⡖⠚⠃⢹⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⣽⣿⣿⢳⣿⣷⣿⣽⣿⣶⣿⠁⠀⠀⢰⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣼⡉⣇⣀⣽⣿⠉⢨⣽⡆⢀⣼⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⣿⣭⣟⡉⠓⠚⠋⣠⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⣿⣿⣿⣿⣇⠈⠛⠛⠿⢿⡟⢋⡁⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣾⣯⣭⣽⣯⣀⡀⠀⠀⢀⡄⠸⡷⠻⣤⠤⢤⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣼⡿⢿⣯⣷⣢⠼⣃⢠⡇⣴⠃⠀⠀⠙⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢛⣿⢻⣿⣿⣇⣾⠿⠛⠛⠻⠦⣹⡽⢡⣤⢤⡀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⢸⠻⣼⣿⡿⣽⠁⠀⠀⢠⢾⠍⢹⣷⠠⣈⡓⣿⡜⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣠⣾⣷⢿⣿⣇⣿⣀⣀⣀⣈⣿⣀⣾⣿⣷⣦⠟⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠟⠾⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⣿⡿⠿⠿⠿⠿⣏⣏⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠷⠀⠀⠀⠀⠀⢠⡿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⣴⣶⣶⣶⣶⣤⣤⣤⣄⣠⣄⣀⣀⣀⠀⠀⠀⠀⣸⣷⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⢿⠀⠉⠉⠉⠉⠉⠁⢰⢻⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⢀⣿⡿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⣴⣶⣶⡶⠶⠶⠶⠶⠶⠿⠿⠾⠻⣿⠹⣏⠉⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢉⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣶⣾⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⣭⡭⠵⠚⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣠⢦⣤⣄⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⣶⣦⡹⣿⣿⣟⣉⢻⡿⠶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⣿⣿⣿⣇⢙⣿⣿⣿⣿⣇⠀⠀⠈⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣏⠀⢀⡏⣿⣾⣿⣿⣿⣿⢻⡇⣶⣦⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣾⣿⢀⣿⠁⠙⣿⠋⢸⠘⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⣿⣿⡼⢻⣄⣠⠏⠀⡿⠀⠛⠛⠿⢿⡿⢷⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⢻⠙⠿⠛⠀⢸⣿⣿⠀⢠⣣⣴⣿⣿⣷⣌⢣⡀⠀⠈⠉⢳⡀⠀⠀⠀ ⣀⡈⣇⢠⠖⢦⢸⣿⣿⣤⣾⠿⣿⣿⡿⠟⠙⡆⢳⡀⠀⠀⠀⢳⡀⠀⠀ ⡟⠿⣿⠏⠀⢸⣇⠙⠛⢫⠏⠀⢨⡟⠁⠀⠀⣷⠀⡷⠤⠤⣤⣀⣷⡀⠀ ⡇⠀⡼⠀⠀⡞⠉⢦⠀⡼⠀⠀⣾⠀⠀⠀⠀⡿⢠⠇⠀⠀⠀⠀⣽⠁⠀ ⣧⠀⡇⠀⠠⡇⠀⠘⡇⡇⠀⠀⡇⠀⠀⠀⢀⡇⣼⣤⢶⢰⣰⣼⡇⠀⠀ ⢸⠀⣇⠀⠀⡇⠀⠀⣧⣿⣤⣾⡇⠀⠀⠀⡾⢠⣿⣿⣯⣿⣿⡿⠀⠀⠀ ⠸⡇⢻⣤⣦⣿⠀⠀⢹⡸⣿⣿⣷⡀⢀⡼⠁⣼⣿⣿⣿⣿⣿⠇⠀⠀⠀ ⠀⢷⢸⣿⣿⣿⡇⠀⠀⢧⠙⠿⢿⣷⣊⠀⠀⠘⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⠀⠘⡆⣿⣿⣿⣿⡀⠀⢸⡄⣠⣾⣿⣿⡟⠳⣄⠘⣿⣿⣿⣿⣿⡄⠀⠀ ⠀⠀⢳⠘⢿⣿⣿⣿⣄⡞⣼⣿⣿⣿⡏⠀⠀⠈⢧⠹⡏⠛⠟⠉⠹⣆⠀ ⠀⠀⠘⣇⠀⠉⠙⠋⠁⢰⠏⠛⠙⣿⠀⠀⠀⠀⠘⡆⢹⡦⠤⠤⣄⣸⣦ ⠀⠀⠀⢹⡄⠀⢠⣴⡄⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⣷⣼⠁⠀⠀⠀⢰⡇ ⠀⠀⠀⠀⢳⡀⢸⣿⣇⢸⠀⠀⠀⣧⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⣼⠀ ⠀⠀⠀⠀⠀⢧⠈⣿⣿⡈⣇⠀⠀⢸⡄⠀⠀⠀⠀⣿⣧⡠⡄⣀⣰⡇⠀ ⠀⠀⠀⠀⠀⠈⠳⣾⣟⣧⠹⣿⣾⣿⣿⡄⠀⠀⡼⢻⣿⣧⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡘⠿⣿⣿⣿⣦⠞⠁⣿⣿⣿⣿⣿⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡀⠀⠀⣀⣤⣿⡿⠿⠛⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠿⠛⠟⠻⠿⠶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣴⡟⢋⠡⣀⠒⠄⠣⢘⠰⣀⠒⢠⠉⡙⠿⣦⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣼⠟⠡⡐⢠⠡⠠⠘⡄⢃⠢⡐⢄⠊⡄⢒⠠⢂⠌⠹⣷⡀⠀⠀⠀⠀ ⠀⠀⢰⣿⠃⡌⢰⠐⠂⡄⣷⣷⠀⡎⠐⠐⠈⣶⣶⠈⠐⠂⡌⠐⠈⣿⡄⠀⠀⠀ ⠀⢠⣿⠖⡐⢈⡄⣢⣴⣿⠿⢋⠐⠤⠡⢡⢁⠹⢿⣷⣦⣁⡌⡑⠤⠙⣿⡀⠀⠀ ⠀⣾⠇⡰⢀⠻⡿⠟⢋⢉⠰⡀⡉⢄⠃⡄⢊⠐⡠⢉⠛⠿⣿⣷⣆⢁⢺⣷⠀⠀ ⠀⣟⡣⠐⣂⠡⠐⣨⣄⠨⠐⡠⢁⣂⣌⡐⡈⢂⢁⠂⣌⣰⣿⡛⡿⣶⣬⣿⢆⡀ ⠀⣿⡁⠥⠐⡈⢅⠈⢻⣿⣷⣶⣿⠟⢉⢻⣿⣶⣾⣿⠟⣰⣯⡹⣦⡙⣿⣿⣧⣽ ⠀⣿⡇⢐⠡⢌⠠⢃⠂⡌⠙⡉⢡⠈⠆⡄⠨⠙⣉⣴⢾⣿⣿⣷⡘⣿⣿⣿⣿⣿ ⠀⠘⣿⡄⠊⡄⠒⡠⠡⠘⡠⣁⣆⣨⣐⣠⣑⣢⣿⡌⢻⣿⣿⡿⣷⢻⣯⢿⣿⣳ ⠀⠀⠘⢿⣄⠘⠤⢁⠢⠑⡐⢛⠛⡛⢛⠛⡛⢛⠠⢿⢰⣻⣯⢴⣹⣿⣼⣻⣾⢧ ⠀⠀⠀⠘⢧⣘⠠⠘⡀⠇⡘⡀⢃⠸⢀⢃⡘⢀⠃⠼⣧⡿⢛⠛⠻⣿⣿⢿⣟⣧ ⠀⠀⠀⠀⠀⠛⢿⢦⣁⡒⠠⢁⠆⠒⠄⠢⠄⢃⠘⣠⣰⡿⢦⣟⣷⣭⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣶⣎⣶⣼⣱⣞⡶⠿⠛⢻⡇⣒⣶⣮⣼⣿⣿⣿⠿ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣳⣜⣦⣝⣾⣿⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⡼⣿⣶⣶⣾⣿⣿⣷⣶⡀⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⣿⠭⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠪⢽⣗⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡯⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠮⣕⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⢾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢼⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⣧⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡳⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡜⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡼⣄⠀⠀⠀⠀⠀ ⠀⢀⡾⡽⠃⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⢳⡹⡆⠀⠀⠀⠀ ⠀⣸⣱⠃⠀⠀⠀⠀⣴⣶⣾⣿⣿⠶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣿⣿⣿⣷⣦⡀⠀⠀⠀⠈⢷⣱⡀⠀⠀⠀ ⢠⣧⡟⠀⠀⠀⠀⠀⠘⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣿⣯⣵⣷⡀⠀⠀⠘⡿⡇⠀⠀⠀ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢻⣍⣿⣄⡀⠀⣳⣿⡀⠀⠀ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⡀⠀⠀⠀⠀⠀⢀⣤⣤⣠⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⠀⢸⣮⠳⡀⠀⠀⠀⢙⣿⣿⣯⠙⠳⣄ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣟⠛⠿⠿⠿⠛⣿⠟⠁⠀⠹⣯⡛⠛⠿⠿⠟⢛⣿⠟⠀⣨⣿⠀⠙⣆⠀⠀⢸⣻⣿⣿⣶⣤⡙ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣶⡾⠟⠁⠀⠀⠀⠀⠈⠙⠷⣶⣶⠾⠋⠁⢠⣾⣿⡙⣧⠀⠈⢳⣠⣾⣿⡿⢛⣿⣿⡿ ⠈⣏⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢉⣿⣿⣿⡟⣧⡀⠀⣿⣿⢑⣿⣿⣿⣷⠁ ⠀⠸⡎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⢸⣿⣿⣿⣿⣮⡇⠀⢿⣿⠘⣿⣿⣿⡿⢀ ⠀⠀⠻⡞⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠙⣧⠀⠀⠀⢻⣿⣿⠿⠛⠻⣆⠘⢧⠀⠈⠉⠭⠒⠈ ⠀⠀⠀⢹⣏⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠘⣧⠀⠀⠸⣿⠃⠀⠀⠀⣙⣆⠀⠀⠀⣠⣤⠄⠀ ⠀⠀⠀⠀⠙⢦⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⣴⠟⠶⣤⣶⠿⣿⢻⣆⢿⣼⣿⣿⠆⠀ ⠀⠀⠀⠀⠀⠈⠱⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⣯⠀⠀⠀⠀⠀⠈⣿⣿⣮⡓⠍⢁⣠⣾ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣭⣢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣀⠀⠂⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⣕⡲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢴⣺⡇⠀⠉⠉⠉⠛⠋⠉⢻⣿⣿⣿⣿⣿⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠬⣿⣖⣒⠤⠤⠤⠤⠤⠤⠤⠤⣐⣒⣾⠯⠗⠛⢻⠥⠀⠀⠀⠐⠀⠀⠀⣼⣿⣿⣿⡿⢛⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠈⣦⣤⠀⠈⠛⠛⠛⠛⠛⢻⣯⣿⡷⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⡻⣆⣀⣀⣤⣀⣀⣸⣿⣟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣋⣀⣀⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⡤⠤⠤⢤⡤ ⣿⣿⣿⠿⠟⠉⠉⠀⣹⣿⣋⣻⣿⡇⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠀⠀⠀⠀⠀ ⠈⠉⠀⠀⠀⠀⠀⣴⡿⠁⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣶⣿⣶⡾⣶⣦⣽⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣯⠿⢿⡻⢿⢿⣿⣽⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣞⣻⣿⡿⢷⡾⢛⣿⣿⠿⣨⢙⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣻⣿⣣⢟⡽⣺⠟⡦⡙⢢⣵⡿⢃⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⡿⣻⣽⣿⡿⣿⢿⣿⣯⠷⢏⠚⠀⣵⣿⡟⢁⣎⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⣵⣿⣿⣿⢿⡿⣿⣶⣵⡪⠝⠀⣠⣿⣿⠋⣠⢣⣾⣿⣷⣶⣶⡄⠀⠀⠀⠀⠀⠀ ⠀⢠⣾⣿⣿⣿⣿⡿⡿⠿⢿⣶⣝⢿⣷⣌⣾⣿⠟⡁⠆⣽⣿⠿⢱⣯⠿⣧⣽⣄⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣽⣿⢻⣽⣿⣿⣶⣌⠻⣧⣽⣿⡿⢋⡘⢠⢃⣿⠿⣟⣽⣿⣟⡶⣥⣻⣳⣦⢄⡀⠀ ⠀⢸⣿⣟⣿⢳⣿⣿⣿⣿⣿⣿⡧⢹⣧⣿⡷⢀⣿⣠⣿⡿⣼⣿⣿⣿⣿⣿⣳⢧⣋⠿⣳⣧⠀ ⠀⣹⣿⣻⣿⣸⣿⣿⣿⣿⣿⣿⣟⣸⡿⣿⡷⢩⡿⣿⣻⣷⣿⣿⣿⣿⣿⣿⢯⡷⣩⠝⡑⢚⣧ ⢸⣟⡿⣷⢿⣧⡙⢿⣿⣿⢿⡿⣣⣿⣿⣿⣧⡿⢧⣿⣿⣿⣿⣿⣿⣿⣿⡯⢏⡳⢅⡲⢌⠢⢼ ⠈⠻⣽⣯⣻⡽⣿⣿⣶⣾⣷⡿⣿⡟⣾⠿⣡⣺⣿⢛⡝⣻⠿⣿⣿⣿⣿⡝⢢⠳⢌⠲⣅⠣⣾ ⠀⠀⢹⣟⡷⣻⢗⣯⣾⠳⣯⣽⢿⣻⠟⣰⣳⣿⡇⡝⢚⠛⡻⣿⣿⣿⡿⣜⠡⡎⣄⠳⣌⣹⡃ ⠀⠀⢸⣯⣷⣽⢿⣿⣿⣿⣮⣿⣿⡟⣸⣳⣿⢹⣷⣭⣎⠱⡒⣬⣽⣿⣟⢢⠏⡐⢄⢻⣼⠇⠁ ⠀⠀⢸⣷⡿⣿⢸⣿⣿⣿⣿⢼⣿⡇⣿⣿⡟⣾⣷⣻⣿⣧⣽⣿⢿⣛⢿⣤⠣⡘⠄⣿⡿⠀⠀ ⠀⠀⠘⣿⣿⡹⣷⣝⡿⣟⣫⣾⡿⣼⣿⣿⣾⡟⢀⠂⠍⠩⠍⢆⠯⣜⠫⢿⣷⡭⣞⣿⠁⠀⠀ ⠀⠀⠀⢹⡿⣿⣮⣽⣛⣻⣻⣭⣾⣷⣷⢟⡫⢅⡢⢜⡠⢁⠜⡠⢉⠌⣹⣾⣿⣿⡟⠁⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⢎⡵⢫⡜⣣⢞⡱⣊⠥⣋⣜⣼⢣⢾⣻⠅⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣾⣧⣛⣦⣏⣲⣥⣾⠶⢛⢥⣣⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣷⢭⠎⡍⣍⠩⣉⠉⢤⠠⡘⡄⢪⣿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡳⣜⢦⣛⡴⡛⢆⢣⠑⣬⣳⡿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⢿⣿⣿⣿⣿⣾⣵⣫⣞⣵⣮⣽⣮⣾⠛⣡⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⣯⢎⡥⣍⠭⣩⢋⡭⡙⢆⠲⢬⣳⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣾⠽⣜⢮⣛⡦⢏⠶⣙⢎⡹⣲⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣾⣯⣿⣽⣯⣾⡽⠶⠟⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣔⡾⠿⠛⠛⠛⠶⠖⣢⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⡀⠀⠀⠀⠀ ⠀⢀⡾⠃⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀ ⢀⡾⠀⠀⠀⠀⣀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠈⠻⣷⣤⣀⡀⠀⠀⠀⢷⡀⠀⠀ ⣼⠇⠀⠀⠘⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⣧⣄⠀⠐⣧⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡙⠛⠢⢤⣿⠤⡀ ⣿⠀⠀⠀⠀⠀⠀⠻⣗⠒⠒⣺⠟⠉⠻⣗⠒⠒⣺⠟⢠⣇⠘⢆⠀⣿⣿⣦⣜ ⢿⡄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠈⠉⠉⢡⢔⣿⣿⢃⠈⢿⣿⣿⣿⡋ ⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠁⠘⣿⣿⣿⣇⢸⠟⠿⠿⠡ ⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠟⠈⠆⠀⢸⡏⠀⣈⣆⠀⢀⣤⠀ ⠀⠀⠈⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⡏⠉⠉⠙⢿⣿⡛⢋⣠ ⠀⠀⠀⠀⠉⠲⣢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡗⠠⠤⠤⢤⣿⣿⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠖⣠⣠⣠⣤⣤⡶⠾⠛⢻⠇⠀⢀⣀⣀⣿⣿⣟⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⣀⡀⣰⣿⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣗⣷⢶⣾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣶⠾⠻⠛⠦⠀⢙⠿⡿⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⠔⣿⡿⡿⡤⠀⠀⢀⡤⠋⢠⠃⠀⠀⠀⠀⠀ ⠀⣠⣾⣿⣿⣿⣛⠷⣄⠀⣴⠟⠁⣠⡾⡵⣶⡀⠀⠀⠀ ⠀⡿⣿⣿⣷⣶⣯⡻⣞⣿⠋⠀⢰⢿⣸⣧⡈⠉⠢⢀⠀ ⠀⡇⣿⣿⣿⣿⣿⡷⣿⣿⢀⣶⣿⣼⣿⣿⡷⠀⠀⠈⢦ ⢸⣿⠈⠻⣿⣛⣛⣵⣿⡿⢂⡾⠿⣿⣿⣿⡇⠀⠀⠀⢀ ⠀⢸⡆⢀⣠⣄⢀⣸⡏⢀⣾⠀⠐⠒⢿⣿⠀⠀⠀⢀⠈ ⠀⢸⣿⣿⣿⣿⡿⣿⣀⡾⣷⣶⣤⣠⡶⠿⡀⠀⢀⡞⠀ ⠀⠘⣿⣿⣯⠭⢽⣿⣿⡶⠏⠀⠈⠁⠀⠀⢸⣦⡼⠁⠀ ⠀⠀⢹⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣀⠉⣿⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣟⣟⠒⠒⠒⠒⠂⠉⠀⢰⡏⠀⠀⠀ ⠀⠀⠀⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡀⠠⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣾⡍⠉⠉⠉⠁⠉⠁⢀⠎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣧⣀⣀⣀⣀⣀⠴⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣄⡇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠿⠿⠛⢻⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠋⠉⠉⠉⠉⠉⠙⠋ ⢸⡿⠿⠋⠋⠀⠀⠀⠀⣿⡿⠉⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢦⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣆ ⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠏⠉⠉⠉⠉⠉⠉⠉⠉ ⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⣿⣿⣿⢿⣿⠛⠿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⣿⣿⠁⠀⠈⠇⠀⢿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⣿⡇⠀⠀⠀⠈⠂⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠻⡏⠁⠴⠟⠟⠻⣦⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡆⠙⢄⠀⠀⠀⢠⠿⢾⣿⠳⢤⡀⠀⠀ ⠀⠀⠀⠀⣶⣿⣿⡀⠀⠳⣆⠀⣠⢾⣻⣿⣿⣷⣿⣄⠀ ⠀⣠⡴⠊⢉⣼⣇⡿⡆⠀⠘⣿⣷⢟⣽⣶⣾⣿⣿⢿⡄ ⡾⠋⠀⠀⣿⣿⣿⣧⣽⡆⠀⣿⣿⢼⣿⣿⣿⣿⣿⢘⡇ ⡇⠀⠀⠀⢹⣿⣿⣿⠿⣷⡀⠻⣽⣮⣙⣛⣻⠿⠋⣻⡇ ⢷⡄⠀⠀⠈⣿⡯⠔⠒⠈⣿⡄⢹⣇⡀⢡⣄⡀⢸⡏⠀ ⠀⢿⡀⠀⢀⡿⢶⣄⣠⣴⣿⢷⣄⣿⢽⣿⣿⣿⣿⡇⠀ ⠀⠈⠣⣴⡏⠀⠀⠈⠁⠀⠘⢾⣿⣿⣮⠭⣽⣿⣿⠇⠀ ⠀⠀⠀⣿⠉⢀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡏⠀⠀ ⠀⠀⠀⠘⡇⠀⠉⠑⠒⠒⠒⠚⣻⣻⣿⣿⣿⣿⡗⠀⠀ ⠀⠀⠀⠀⠹⡤⢀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠁⠀⠀ ⠀⠀⠀⠀⠀⠱⡄⠈⠉⠉⠉⠉⠉⢩⣷⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠦⣀⣀⣀⣀⣀⣼⠟⠁⠀⠀⠀⠀⠀
⠀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⠀⠀⠀⠀⠀⠀ ⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⣿⣿⣶⡆⠀⠀⠀⠀ ⣿⣿⣄⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⠈⠻⢿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⠿⠇⠀⠀⠀⠀ ⠀⠀⠀⠙⣿⣿⠛⠛⠛⣿⣿⠛⠛⠛⢻⣿⠛⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⣀⣀⣀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣤⣤⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠛⠛⣿⣿⣿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡀⣈⡉⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⣧⣉⠁⣠⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣷⡀⠀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⣿⣿⣿⣿⣿⣿⡟⢁⣾⣿⣿⣦⠈⢿⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠛⠛⠛⠛⢉⣴⣿⣿⣿⣿⣿⠇⢸⠀⠁⠶⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⡉⠙⠛⢁⣠⣿⠀⡇⣴⠄⣁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠑⢠⡤⢉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣄⠉⢉⣠⠈⠛⠒⣤⡈⠛⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⡄⢻⣧⠀⠀⠈⣴⠙⣂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⢸⡄⠹⣇⠀⠀⢠⣦⠈⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠟⠀⠹⣆⠀⠀⠠⣦⠈⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⣶⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠶⠀⣠⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡸⠿⣿⣿⠿⠀⠀⠀⠀⠀⠀⢀⢴⠀⠀⠀⠀⠀⠀ ⢠⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢾⠶⠤⠶⠴⠶⠆ ⠘⡟⠁⣩⡿⠋⠉⠀⠀⣿⣿⠿⠻⣿⣿⡇⠀⠀⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠷⠞⠁⠀⠀⠀⠀⣴⣿⠏⠁⠀⣿⣿⡇⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⣀⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⠃⠀⠀⠀⠀⣀⣀⣀⣀⣀⣰⣟⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠻⣿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀ ⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢷⣴⢹⠇⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠙⠾⣀⣀⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠻⢿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡴⣖⢲⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣋⡉⠁⠙⠓⠒⠶⠦⣤⣤⣄⠀⠀⠀⠀⢀⡤⠴⠒⠚⠋⠛⠛⠛⠒⠒⠒⠦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠳⢿⣟⣻⣿⣂⣶⣦⣤⣤⣀⡈⠃⣷⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡿⡟⣿⣿⣿⣮⠉⢩⡟⠳⠿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠓⠒⡎⢛⣿⣿⡃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣷⠠⣿⣿⣶⣿⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣾⢿⣿⣿⡿⠁⠀⠀⠀⠀⠈⢀⣿⣦⡀⠀⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠐⢁⡀⣾⣿⠛⠀⠐⣿⡿⠃⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠸⠟⠹⣧⠀⠀⢀⣻⠇⠸⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠳⢤⠴⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠘⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⣿⡀⠀⠀⠀⠀⠀⢠⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⣗⣀⠀⠀⠀⢀⡞⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣟⣇⠈⠛⠳⠶⠖⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣾⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣾⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣷⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡶⣄⣀⡀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠽⠟⠋⠀⠀⠀⠉⠉⠉⠋⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⢘⣀⠀⣷⣿⣤⠴⠛⠓⠒⠒⠊⠒⠀⠀⠁⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢷⣄⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⢾⣡⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠸⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡤⣤⣤⡀⠀⣠⠈⣷⡀⠀⠀⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⡿⠁⠀⠀⠀⠀⣀⣀⣀⣀⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠟⠉⠀⠀⠀⠉⠙⠿⣧⣀⣹⣧⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⡇⠀⢸⣿⣿⣁⣀⢀⡤⠞⠛⠉⠉⠉⠛⠳⢾⣝⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⣠⣴⠦⠀⠀⠀⠀⠀⠘⣿⠉⢻⡄⠀⠸⣿⠀⢰⡀⠀ ⠀⢸⡇⠀⣸⣿⡇⠀⣽⠟⠁⠀⠀⠀⣀⣤⣄⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣀⣾⡀⠀⠀⠀⠀⠹⡆⠈⣷⠀⠀⣿⡀⢸⣇⠀ ⠀⣸⡇⠀⣿⣿⡷⣾⠋⠀⠀⠀⠀⢸⣿⣿⣄⣰⣆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠙⠃⠀⠀⠀⠀⠀⡇⠀⣿⣇⠀⣿⡇⢸⣿⠀ ⠀⣿⡇⢰⣿⣿⡧⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠶⠀⠀⠀⠀⠀⢠⡇⠀⡿⣿⠀⣿⡇⢸⣿⠀ ⠀⣿⡇⣸⣿⣿⠃⣿⠀⠀⠀⠀⠀⠘⢶⣿⣿⣥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⢸⡃⣿⣦⣿⣧⣿⣿⠀ ⠀⣿⡇⣿⣿⣿⠀⠘⣇⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣮⣹⣄⣸⣷⠿⠁⠙⠻⢿⣿⠀ ⠀⣿⣇⣿⣿⣿⡀⠀⠈⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢀⣾⡟⠁⠀⡀⠀⠀⠀⠈⢧ ⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⣹⣶⣦⣴⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡁⠀⠀⢠⣿⣿⠁⣠⣾⣿⣷⣤⠤⡀⠀ ⠀⢿⣿⣿⣿⣿⣿⡀⢀⡴⠛⠁⠀⠀⠀⠉⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠳⠀⣰⣯⣾⠉⠀⢿⣿⣿⣿⣿⣿⠀⠀ ⡆⢸⣿⣿⣿⣿⠻⢷⡉⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⢀⣼⣿⣿⣿⢸⠀⡘⢿⣿⣿⣿⡟⡀⠀ ⣿⠈⣿⣿⣿⣿⡄⠀⢿⡄⠀⠀⠀⢀⣀⣴⠞⠁⠀⠀⠈⠉⠒⠂⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⣧⠈⠑⠶⠶⠒⠉⠀⠀ ⣿⣆⢻⣿⣿⣿⣿⣶⣦⣿⡀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⡜⣇⣀⠀⠀⠀⢄⣀⣴ ⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢸⣿⣿⣿⣿⡿⠸⣿⣤⣤⣤⣼⣏⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠿⣿⢸⡿⢿⢿⡿⠀⡜⢿⣿⣿⣿⡿⣸⡿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⠲⣶⣤⣄⣀⠀⠀⠀⠀⠀⣀⣠⣶⡾⠋⠀⠀⣿⣿⣿⡆⣾⣿⡀⠈⢲⡿⢯⠭⠴⡟⠀ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢀⣿⣧⣬⣎⡞⣿⣟⣶⣶⢔⡠⠈⠀⡟⠀ ⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠀⠀⠀⣠⠔⠛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠁⠀⡀⠁⠀ ⠀⠀⢿⣿⣿⣿⣿⣿⡌⠻⢿⣆⠈⠉⡠⢉⣿⠋⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⣠⠿⢿⣿⡏⠉⠉⠙⣿⣿⠁⠀⠀⠉⠁⠒ ⠀⠀⠘⣿⣿⣿⣿⣿⣷⡀⠀⠉⣳⣆⣴⠏⠁⠀⠉⠙⢦⣄⡀⠀⠀⢀⣠⡴⠚⠋⠀⠀⠀⣰⠃⠀⠀⢙⢷⡀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⠀⠐⣻⡞⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠸⣦⣤⠔⠁⢸⣧⣤⣾⣿⣿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣧⣠⡟⠀⠤⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣄⠀⢸⣷⠢⠴⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⡤⣤⠤⣾⣿⣽⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣠⣤⣤⣀⠀⣀⣼⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆ ⣼⣿⣿⣿⣿⣧⣤⣿⠿⠉⠿⠿⠿⠛⠛⠛⠛⠛⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠶⠶⠶⠶⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣾⣿⣿⣤⣤⣤⣤⣤⣤⣤⣼⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⠜⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠉⠿⠏⠉⠉⠉⠉⠉⠙⠛⠛⠃ ⢸⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⣿⣿⣿⠟⠉⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠛⠉⠉⠙⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠃⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣶⣾⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⡟⠙⠻⣿⣿⡿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⡟⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡀⠀⠀⠹⣇⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠻⣦⣄⣀⣉⣳⣦⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡴⠖⠋⠉⠉⠉⠉⠓⢦⣀⡤⠖⠚⠉⠉⠙⠳⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠔⠁⠀⠀⣀⣠⠤⠤⢤⣤⣀⠐⡀⠀⣀⣀⣀⣀⣀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀ ⠏⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣬⣽⣿⣏⠉⠉⠈⠉⣉⣙⣳⣞⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⡴⠞⠛⠉⠁⠀⠀⠈⠉⠻⣶⠞⠛⠉⠉⠉⢉⠉⠛⢷⡀⠀⠀⠀ ⠀⠀⠀⢰⣿⡉⠀⠀⠀⠀⠀⣶⣿⣷⠄⠀⣿⠀⠀⠀⠀⢀⣿⣿⡆⠀⣿⣤⠀⠀ ⠀⠀⠀⠀⠉⠙⠳⠤⣤⣀⣀⣈⣙⣁⣤⣴⡿⠤⣤⣤⣤⣤⣿⣽⣧⣴⡿⢿⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠛⣋⡿⠟⠉⠀⠀⠀⢀⡀⣀⣠⣤⣿⡿⠛⠃⠓⠳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣾⡯⢀⢠⣶⣶⡌⢹⣾⣿⣿⣽⣾⣿⡇⡌⣶⣶⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠘⠘⠻⠟⠃⠀⢹⣿⣿⣿⣿⣿⣇⠘⠙⠋⠀ ⠀⠀⢀⣤⡶⢻⣿⣛⣻⣿⣿⡿⠷⠶⠲⡖⠒⠚⠛⠛⡿⠛⠛⠛⣻⡏⠀⠀⠀⠀ ⠀⠀⠘⢿⣀⣈⣉⣉⣿⠟⠻⣷⣶⡀⢀⣤⣐⣦⣤⣶⣿⣿⣿⡿⣿⣿⣀⣀⣀⠔ ⠀⠈⠳⢮⠉⠉⢹⡟⠁⠀⠀⣿⣿⡇⣿⣿⡿⠟⠛⠙⢿⣿⡏⠈⠙⢂⠀⠀⠀⠀ ⣀⡀⠀⠀⠀⠀⢸⡄⡀⠀⠀⣿⣿⣇⣿⠁⠀⠀⠀⠀⢸⣿⡇⠀⣠⠆⠀⠀⠀⠀ ⠿⠿⢷⣤⣭⣭⣽⣿⡁⢀⣴⠟⠿⠿⠿⣶⣄⣀⣀⣄⣼⣿⠏⠉⠹⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡅⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⣰⠇⠀⠀⠀⠀
/\__/\ (⌐■ᴗ■) | >ᡕᠵ᠊ᡃ່࡚ࠢ࠘ ⸝່ࠡࠣ᠊߯᠆ࠣ࠘ᡁࠣ࠘᠊᠊ࠢ࠘𐡏 | __ | \/ \/
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⣀⣀⣀⣰⣦⣼⣟⣛⣯⣭⣽⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢛⣿⣛⣛⣛⣻⣟⣛⡛⠛⠻⠿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⡆ ⢰⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⣿⡿⠿⢹⣀⠨⣿⣿⣿⡿⠿⠿⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢶⣶⣶⠼⣦⣤⣼⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣯⠿⠟⠛⠻⢶⣿⣯⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣺⡿⠿⠷⠶⠒⢶⣶⠖⠀⠉⡻⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⢻⣭⣫⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣖⡿⠋⢙⣿⠿⢿⠿⣿⡦⠄⠀⠀⠀⣠⣾⠟⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣰⣿⣴⣿⡿⠿⠿⠿⢿⣦⣄⠀⠀⠀⣠⣾⣿⠃⠀⢀⣸⡿⣳⣶⣲⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣽⡿⣛⣵⠾⠿⠿⠷⣦⣌⠻⣷⣄⢰⣿⠟⠁⠀⢠⣾⠿⢡⣯⠸⠧⢽⣄⠀⠀⠀⠀⠀ ⠀⢸⡇⡟⣴⡿⢟⣽⣾⣿⣶⣌⠻⣧⣹⣿⡿⠋⠀⠀⠀⣾⠿⡇⣽⣿⣄⠀⠀⠉⠳⣄⢀⡀⠀ ⠀⢸⠇⢳⣿⢳⣿⣿⣿⣿⣿⣿⡆⢹⡇⣿⡇⠀⡆⣠⣼⡏⢰⣿⣿⣿⣿⣦⠀⠀⠀⠈⠳⣅⠀ ⠀⣸⡀⢸⣿⢸⣿⣿⣿⣿⣿⣿⡇⣸⡇⣿⡇⠀⡟⣻⢳⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣧ ⢰⡟⡿⡆⠹⣧⡙⢿⣿⣿⠿⡟⢡⣿⢷⣿⣧⠾⢠⣿⣾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠘ ⠀⠻⡽⣦⠀⠈⠙⠳⢶⣦⡶⠞⢻⡟⡸⠟⠁⢠⠟⠉⠉⠙⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡴ ⠀⠀⢸⣿⡇⠀⠀⣀⣠⠀⢀⡀⠸⣹⠇⠀⣰⡟⡀⠀⠈⠛⠻⢿⣻⣿⡿⠀⠀⠀⠀⠀⠀⡠⠁ ⠀⠀⢸⣿⣇⣴⢿⣿⣿⣿⣮⣿⣷⡟⠀⣰⣿⢰⠀⣀⠀⠀⠀⢀⣉⣿⡇⠀⠀⠀⠀⠀⣸⠃⠀ ⠀⠀⢸⣿⡟⣯⠸⣿⣿⣿⣿⢈⣿⡇⣼⣿⠇⣸⡦⣙⣷⣦⣴⣯⠿⠛⢷⡀⠀⠀⠀⣰⡟⠀⠀ ⠀⠀⠘⣿⣿⡸⣷⣝⠻⠟⢋⣾⣟⣰⡏⣠⣤⡟⠀⠀⠌⠉⠁⠀⠀⠀⠀⢻⣶⠀⢀⣿⠁⠀⠀ ⠀⠀⠀⢸⡿⣿⣦⣽⣛⣛⣛⣭⣾⣷⡶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⢸⢻⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣀⣀⣀⣀⣀⣠⣤⠶⠛⠁⢀⣾⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣻⣿⣿⣿⣿⣿⣿⣎⣿⡅⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡷⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠻⢿⣿⣿⣟⣂⣀⣀⣀⣀⣀⣀⣤⠴⠋⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣷⡄⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣤⣤⣤⣤⣄⣤⣤⡤⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢐⡠⠤⠐⠒⠓⠓⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⡈⠥⠀⣄⠈⠘⣇⠀⠀⠈⠣⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢷⠀⡀⠀⠀⢀⡈⢤⡾⣾⣆⠟⠻⡀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣿⣟⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠸⠀⠀⠴⠀⠂⢉⡐⠤⡙⠬⡀⠘⠄⢿⣌⠈⠀⡇⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠄⠘⢿⣷⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠐⠀⢤⠘⡀⠁⣁⢁⡀⠠⢊⢽⣾⠿⠉⠀⠀⠈⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⣀⠀⠀⠁⠞⠁⠁⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠘⠰⠀⠘⢭⢻⣄⢻⣟⣞⣮⢻⣿⣷⣦⡀⠳⣮⣀⠠⠉⢀⡀⠡⠉⠄⠤⢐⡉⣰⣯⣆⢻⠏⢰⢫⣿⢏⣶⣿⠊⢠⡟⣰⣿⢣⣿⠿⠛⣹⣿⣿⣿⠋⡼⢿⣿⣞⡿⢛⣷⣬⡻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠠⠀⠀⠁⢀⡀⠸⣧⣟⢷⣹⡿⣿⣧⡽⣿⣿⠣⠀⠀⢭⡛⠓⠲⠶⠶⠾⠚⢛⡋⢰⣿⣿⣿⡾⢠⣿⣿⣷⣾⣿⠋⡰⠎⣰⢿⡟⣿⣏⣤⣴⣿⣿⣿⣿⣖⡡⠾⣽⠿⣠⣾⣿⣿⣷⠏⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠉⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠣⠐⠀⣾⠁⠀⠙⢿⣯⣥⣇⣸⡛⢿⣎⢿⣇⡀⠑⠦⠴⠋⢀⣠⣤⣈⣉⡛⠃⠘⠿⢿⣿⣧⣾⣿⣿⣿⣿⠏⢠⠉⢠⢏⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣾⡯⣿⣟⡜⠀⣸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⣀⡁⠀⢰⠏⢀⡇⠀⠀⠙⣿⣿⣿⣿⡄⢻⣿⡿⠘⡄⣆⣴⠾⢟⣭⣛⣿⠿⢿⣷⣶⣶⣤⣄⣈⠉⠉⠛⠿⠿⢀⢃⠂⡌⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣧⣿⣏⠀⠀⣹⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⣿⡀⢸⠁⠀⣶⣶⣜⢿⣿⣿⣿⡀⡿⢐⡉⣼⢫⣷⣦⡙⢯⣿⣿⣿⣷⣶⣿⣿⣭⣟⠛⠻⢷⡹⢦⡄⢈⠆⠀⡗⡜⣿⣿⣿⠛⣻⠿⢿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡏⠀⣾⣿⣿⣿⠿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⡈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⢠⡟⣇⠈⠀⠀⣿⣿⠿⣿⣿⣿⣿⣱⢁⠆⣸⢳⣿⡿⢿⣿⣌⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⢝⣧⡇⠨⢌⠀⡇⠲⡘⣿⣿⡿⠁⣠⢿⣁⣴⣿⠛⣉⣻⣿⣿⣿⣿⠋⠀⢰⣿⣿⣿⢱⡇⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡲⡍⢙⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠘⠃⣻⡆⠀⠀⢻⣿⣶⣿⣿⣿⣿⠇⡈⢠⢣⣿⣿⣷⣬⡙⢿⣶⣝⢿⢿⣿⣿⣿⣿⣿⡟⠛⠛⣾⡏⣷⠨⢄⠀⢡⢃⠱⠼⣿⠁⠞⣱⣿⣿⣏⣄⣨⣬⣿⣿⣿⠟⠁⣠⡄⢸⣿⣿⡟⣾⣟⣿⢼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠌⠈⣗⡲⣖⢮⡳⣝⢦⡜⠀⠀⠀⠀⠀⡈⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡆⠀⢠⡝⡇⠀⢸⣕⢽⡻⣿⣿⣿⡏⠤⠁⣾⣿⣿⣿⣿⣿⣿⣷⣿⡿⢮⣎⢿⡏⠹⣿⣿⣿⡟⣴⣿⢹⣿⠰⢈⠀⠀⢎⡘⡰⠁⢂⡼⣛⢿⣿⣿⣿⣿⣿⣿⠟⠋⠀⢠⣿⠇⣸⣿⣿⢣⠻⣸⢽⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡐⠸⡵⣫⢞⡵⣫⠞⠀⠀⠀⠀⠀⠐⠠⠐⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣾⣿⣿⣿⣷⡀⠀⢻⣧⠀⠘⣿⣷⣿⡽⣿⣿⢁⠃⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣍⣺⡇⠀⣿⣿⣿⣹⣿⣿⣾⣿⠘⡤⠀⠀⢢⠑⠀⢠⠉⢋⣾⣕⢄⡻⣿⣯⣿⣿⣴⣶⠀⣾⠏⢰⣿⣿⣣⣶⣿⣿⢸⣾⠟⣰⠀⠀⠀⠀⠄⠀⠐⠀⠀⠠⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠙⣵⢫⡞⣵⠂⠀⠀⠀⠀⠀⡁⠂⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⡿⢛⣩⣥⣬⣥⡀⠈⠛⠧⠀⢸⣛⠻⠿⢿⡅⡎⠀⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡇⣿⣿⠈⣧⠀⠁⠀⠀⠈⢀⠠⢣⠝⣿⣷⣯⣒⣽⣿⣿⣿⡿⠀⠁⣠⣿⣿⣿⣿⣿⡿⡣⣿⠋⣰⡟⢸⡀⠀⠀⢀⠠⠀⠀⠂⠀⠀ ⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠉⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⢷⣶⣦⣤⣄⣐⠈⠁⠘⠿⣻⣟⡿⣽⡄⠀⠈⠀⠀⠀⠄⠌⣁⠣⠁⠀⠻⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⠿⢿⢰⢧⣿⢫⢇⣿⡄⠀⠄⠀⠉⢆⡑⠣⠞⠉⣉⢴⣿⣿⣿⣿⣿⢡⣶⣾⢟⣿⣿⣿⣿⣿⢅⠞⣡⣾⡿⢃⣿⣿⡀⠀⠀⢀⠀⠂⢀⠈⠀ ⠀⠀⡁⠐⠀⠁⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣦⠘⡙⠛⡟⢡⣾⢿⡆⢄⠙⠺⣽⣻⣷⠀⠀⡀⠀⠀⠠⢄⡀⢀⣀⠀⢡⣕⠯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣰⣾⣿⡇⡿⣾⡏⡞⠸⣿⠇⠀⠀⠆⢠⠀⠈⠀⠀⠀⠹⣶⡝⢿⣿⣿⡇⢸⢟⣥⣏⣿⣿⣿⠟⠋⣠⣾⣿⠟⢁⣾⣿⣿⣧⠀⠀⠠⠀⠄⠀⡀⠂ ⠀⠠⠀⠐⠈⢀⠀⠄⠁⡐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⣿⡛⠟⣰⣶⢿⣫⣟⣷⠨⣿⡀⠀⠙⢦⢣⠀⠐⡀⠀⠎⡠⢀⣂⠉⢆⠀⠈⠛⢆⠘⠿⣿⣿⣿⣿⣿⣿⣿⡉⠻⣿⣿⣿⡿⣸⣣⡿⣼⢡⡷⠋⣰⠂⠀⠈⠅⢎⡰⢁⠎⡰⠀⠀⠙⠦⡬⠟⠀⠾⠿⠟⠛⢋⣁⣤⣴⣿⣿⠿⢋⣴⣿⢣⣿⣿⣿⡄⠀⠄⠐⠀⡐⠀⠀ ⠀⠐⠈⠠⠈⡀⠄⠂⠐⢀⠐⠀⡐⠀⠀⠀⠀⠀⠀⣀⠔⢿⣯⢿⡇⠻⢃⣌⢿⣽⣻⡾⣽⢾⡆⣟⣷⡀⠀⠀⠫⡤⠀⠡⢀⠐⠑⠢⢍⡶⣌⠐⠂⡄⠈⠂⠀⠠⢉⠻⢿⣿⣿⡟⠿⣦⣸⣿⣿⢣⣷⡿⣴⠇⣼⡇⣿⣿⠀⠄⠀⠀⠊⡔⢩⠘⡌⢶⠈⢶⣤⣤⡀⠀⣀⣶⣶⣿⣿⣿⣿⠿⠋⣡⣴⠹⣾⡍⠐⣾⣿⡿⣧⠀⠠⠈⡀⠄⠠⠁ ⠀⠡⠈⡀⢁⠠⠐⠈⡀⠂⠠⠁⠠⠈⡐⠀⠀⠀⠺⣌⠻⣄⠻⠟⢁⠰⣿⣿⠂⢛⣓⡛⠯⣿⣳⡜⢷⡷⣄⠀⠀⠱⣃⠀⠀⠄⠀⠐⠀⠀⡉⠛⠦⠐⡡⢀⠀⠀⠀⠊⡄⠉⠛⠳⣴⣿⠿⣫⣵⡿⢻⢟⡿⢠⣿⡧⠉⣨⣆⠊⠄⠀⠀⠀⠀⠉⠰⠈⠿⢿⣿⠟⢁⠾⠟⠋⠉⠟⢛⣉⣤⣶⣿⣿⣿⢰⢯⠃⢧⡿⠛⣱⣿⠀⠀⡁⠠⠐⢀⠂ ⠀⠂⢁⠀⠂⠄⠂⢁⠐⠈⠠⠈⠄⢁⠠⠈⡐⠀⠀⠈⠳⡌⣁⠰⢾⡇⢽⣻⡇⢦⡑⠌⠳⢤⣍⡙⠘⢛⡩⢖⡄⠀⢧⠀⠀⠀⠀⠀⢸⢓⡄⡀⠐⠠⠀⠁⠈⠐⠀⠀⠈⠑⠠⢄⠉⠛⡎⣫⣭⣶⡿⠟⢁⣾⠞⠀⡰⣮⡻⠈⡜⠀⠀⠀⡁⠂⠂⠁⠀⠈⠀⠀⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣷⢸⢯⠀⡵⠂⢀⣿⣿⡆⠀⠄⢁⠐⡀⠂ ⠀⡁⠂⢈⠐⠠⠁⢂⠈⠄⡁⠂⠌⢀⠐⠠⠐⢈⠀⠀⠀⠘⣬⠳⣌⠒⠾⣽⡇⢸⢿⣦⠘⢣⢎⡼⣙⢮⢱⢫⡜⣱⢨⣃⠄⠀⠀⠀⠀⠆⣐⠀⠍⢳⠲⣄⣁⠀⠀⡀⠀⠀⠠⣀⠈⡉⢈⠉⡉⠠⢴⣞⣯⠟⠀⢼⣿⣮⣟⠆⠠⢃⠄⠀⢫⣙⠹⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠌⠇⠈⠀⠀⣹⣿⣿⡇⠀⡈⠄⠐⡀⠂ ⠀⠄⡁⠂⠌⠠⢁⠂⡈⠄⡐⠈⠄⢂⠈⡐⢈⠠⢈⠐⡀⠀⠀⢫⠔⢮⡱⢆⡆⠘⣜⠳⠀⢦⣘⠀⠭⡲⡍⠶⢉⢒⡣⢎⡓⢦⣀⡀⠀⡆⠱⠀⢰⡈⠑⢎⡖⡳⢆⡄⠀⠀⢂⡀⠁⠘⡄⠣⢌⡑⠆⠀⠀⢠⠒⡞⠻⠿⣿⣧⠱⣈⠢⠀⠀⠊⠕⠣⠻⠿⣿⠿⣿⠿⡿⢿⠿⡿⢿⡿⣿⣿⣿⡿⠟⠁⠀⣠⣴⣿⣿⣿⣿⣇⠀⠐⡈⠐⡀⠡ ⠀⠂⠄⠡⢈⠐⡀⢂⠐⠠⢀⠡⠈⠄⢂⠐⡀⠂⠄⢂⠐⠠⠀⠀⠉⠶⣙⡘⢆⠀⢏⡞⠀⣣⢎⡅⠰⡔⡔⢮⡜⣣⠝⡀⡝⢦⠳⣜⡀⠱⡀⠁⡀⠽⡄⠀⠘⠱⢫⡜⡥⠈⠄⠐⠄⠀⠀⡃⢆⠀⠀⠤⡃⢆⠱⣈⡑⠂⢨⠙⡳⢄⠃⠥⠀⠈⠽⣠⠠⠀⣤⣤⣶⣶⣶⣴⣶⣿⣶⣷⣶⣿⣯⡴⠖⣠⣾⣿⣿⣿⡿⣿⣿⣿⠀⠐⠠⠁⠄⡁ ⠀⠡⡈⠐⠄⢂⠐⠠⢈⠐⡀⢂⠡⠈⠄⠂⠄⠡⠈⠄⡈⠄⡁⢂⠀⠀⠱⢩⠆⠀⢩⢞⠀⡱⣎⠆⢸⢱⡙⢦⡙⢦⡛⢀⡝⣎⠳⡜⢲⡀⢉⠤⢄⠘⠿⢄⠀⠄⠀⠈⠓⠆⠉⢆⠈⠢⠀⠀⠑⠊⠑⠀⠙⠀⠀⠀⠀⢀⠄⡣⡐⣌⠘⠄⠃⠀⠈⢡⢏⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣩⠔⢉⡿⠿⢛⣻⣿⣷⠙⣿⡿⠀⠈⠄⡁⢂⠐ ⠈⡐⠠⢁⠊⠄⡨⠐⢂⠐⡐⡀⢂⠡⢈⠔⡈⠄⢃⡐⠀⠆⡐⢀⠢⢀⠀⠈⠂⢘⠰⢪⠀⠱⡎⡇⠘⡦⡝⢮⡙⣦⠹⢐⠺⣌⠳⣄⠑⠂⢠⠀⡄⠢⡌⠿⠠⠀⡄⠻⠜⠂⠨⢄⠃⠆⣈⠑⠤⣁⢂⡠⠤⠴⢖⣒⣊⣉⣭⣭⣭⡴⠶⠂⠁⠁⡀⠀⠘⢜⡈⢳⢿⣿⡿⠛⠉⠀⢉⣤⡾⢋⠀⢀⣴⣶⣿⣿⣿⣿⣿⡏⢹⠇⠀⡁⠢⢐⢀⠊ ⠐⠠⡁⢂⠌⡐⠠⣁⠂⠌⡐⠠⢁⢂⠢⠐⡠⠘⠠⡀⠍⡐⢠⠈⡐⠤⠈⠄⠀⠀⠘⠥⠀⢘⡱⡃⠀⢧⡙⢦⣙⢦⠋⢈⠷⣬⢓⠮⠂⢀⡘⠀⢧⠄⢹⣄⠙⢀⠱⠠⡄⠲⡜⢂⠉⠒⠀⠒⠠⣄⣈⠉⠉⠉⠉⠉⣉⣉⣉⣠⠤⢄⠲⣰⣾⣽⣿⣤⡀⠀⠉⠀⠘⢿⣷⣶⣦⡶⠛⢁⡴⠃⣠⣿⣿⣿⢿⣿⣿⣿⣿⣿⢃⡇⠀⠄⡁⠆⠂⡌ ⢈⡐⠄⠡⢂⠌⠡⡀⢌⠰⢀⢃⠰⢀⠢⠡⠄⢃⠡⠐⢂⠌⠄⣂⢁⠂⡉⠤⢁⠂⠀⠀⠀⠈⠱⡁⠀⢃⡉⣈⢀⡀⢀⡍⡞⠔⠉⠀⠀⠀⠱⠀⡚⠆⠈⢈⠳⢌⣂⠀⠹⢆⠑⠮⢯⡝⣮⡁⠇⡔⢮⠳⠈⠉⠉⢁⠛⡋⢍⠀⠀⣨⣶⣿⣿⣿⣿⣿⠟⠂⠀⠀⠈⠈⠻⠟⠋⡠⡜⠃⠂⠚⠛⠟⢫⣶⣿⣿⣿⣿⣿⣿⣆⣷⠀⢂⠡⠘⡠⠐ ⢀⠰⢈⠁⠆⣈⠂⣁⠂⠆⡈⠄⠒⡈⠤⢁⡘⠠⠌⣁⠢⢈⠂⢄⠂⣁⠒⡐⡈⠄⢃⡐⢀⠀⠀⠀⢀⠸⢲⡍⠮⢁⣚⠜⠁⠀⠀⢀⠰⡀⠄⡀⢈⡐⢌⠠⠘⡄⢢⢉⠤⠉⠐⠤⡄⢠⠀⠉⠀⠀⡀⢀⠀⠄⡘⠀⢁⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⠁⠀⡐⢈⠰⠀⠀⢠⠴⣙⠂⡴⠻⣛⣽⣾⣿⣷⣶⣯⣻⣿⣿⣿⣿⡏⣿⡆⠀⢂⠑⣀⠃ ⢀⠒⡈⢌⠰⠠⠘⠠⠌⢂⡁⠎⢡⠐⢂⠡⣀⠣⠐⠄⠢⡁⠜⠠⡘⠀⢆⠰⠠⢉⠤⢀⠃⡌⠠⠀⠈⠀⣷⡶⠞⠉⠀⡀⠄⠂⢀⠂⠆⡐⠀⣄⠀⠈⠂⣀⠃⠘⠄⡊⠔⣉⠒⡛⠜⠀⡀⢄⠢⡑⠌⠀⢀⣔⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⡅⠀⠐⡈⠔⢂⠀⢠⠏⣜⠁⢎⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣷⠀⢀⠊⠄⡌ ⢀⢊⠐⡄⠢⢁⠩⠐⠌⢂⠰⠈⡄⠊⡄⠡⠄⢂⡉⠰⢁⠰⢈⠡⠐⡉⠄⠢⠑⢂⠰⢈⠰⢀⠃⡌⠠⠀⠀⠀⢀⢀⠒⢠⠁⠀⠠⢡⠘⡀⢰⣏⡟⣦⢤⣀⠈⠐⠀⠀⠡⠄⡁⠠⢀⠢⡘⠄⠁⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢋⢡⡘⢎⠀⠀⡤⢄⠈⠀⠀⣏⠞⡌⡜⣾⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⠋⣼⣿⡟⠀⠠⠘⡀⠆ ⢀⠢⠁⡄⠃⡌⠐⡉⠄⠃⡄⠃⢄⠃⠄⢃⡘⠠⠐⣁⠊⡐⡈⠄⢃⠤⢉⡐⠉⡄⠢⢁⠒⡈⠰⢀⠃⡡⢊⠐⡈⠄⢊⠄⠀⣆⠐⢂⠰⠀⡼⣺⡝⣞⣳⣭⣟⡳⢶⠀⠀⡀⠀⠁⠈⠂⠁⠆⠻⣿⣿⣿⣿⣿⣿⡿⠟⢫⠉⡔⢢⢉⠆⠣⠘⠀⢀⠼⣘⠧⣣⠀⠀⣮⢹⢰⢳⣿⣿⣿⣿⣿⠏⠀⢸⣿⣿⣿⢉⣿⠃⣰⣿⡿⠁⠀⠄⢃⠰⢈ ⠀⠆⡑⢠⢁⠢⠑⡈⠌⠒⡠⠉⡄⠊⠌⠤⠐⡡⢁⠢⠐⠡⢄⡉⠄⡂⠆⢠⠃⠤⠑⢂⢂⠡⡁⠆⢡⠐⠤⠡⠌⡘⠠⠀⣼⣟⢷⣀⠀⠰⣏⢷⣹⡭⣗⣳⠾⣽⠃⢀⠡⡐⠄⠢⠐⠄⡂⢄⠠⢀⠀⠀⠀⠀⠀⠉⠘⠃⠉⠈⠀⠀⠀⠀⠀⠂⠋⠚⢥⡛⡴⠀⠐⡬⠃⡞⣮⢻⣿⣿⠟⠁⢠⣷⡈⢻⣿⣿⢠⠇⣴⣿⣿⠃⠀⠌⡰⢁⠂⠆ ⠈⡔⢁⢂⠂⠆⡑⡈⠔⢡⠐⡡⠐⣉⠰⢈⠡⡐⢂⠡⡉⠔⠂⠤⠑⡐⠌⢂⠌⡰⢁⠊⢄⢂⠡⡘⠠⠌⢂⠡⢂⠡⠀⣰⡍⠹⣌⢿⣦⡀⠉⠻⢶⡽⣣⢯⣻⡅⠀⠄⡂⠅⢊⠁⠈⠀⠁⠂⡌⠄⠀⠀⠀⠈⠹⡍⢧⡙⣇⡛⢦⡓⣖⠲⣆⡔⡀⠀⠀⠈⢱⠂⠀⡵⠀⡇⣿⣷⡻⢋⠀⣠⣿⣿⣷⠘⣿⡏⠀⣼⣿⣿⡏⠀⠄⢃⠰⢀⠃⡌ ⠐⡰⠈⡄⢊⠔⢠⠁⠎⡀⢆⠡⡘⢀⠆⠡⠒⢠⢁⠒⡐⠨⡁⠆⡑⡈⠔⡁⢢⠐⢂⡉⠄⠢⡁⠔⢡⠘⡠⢁⠆⠁⠀⣿⣧⣤⡘⣎⠻⣿⢶⢠⣀⠉⠙⠳⠳⠀⠠⠘⠠⡘⢠⠘⡠⢁⠎⡐⠄⠂⠀⢀⠀⠀⠀⠙⠀⠒⠀⣭⣤⣽⣌⣳⣘⣜⣱⣲⠄⠀⠀⠉⠀⢹⠀⣷⣌⠛⠡⠉⣰⣿⣿⣿⣿⡆⢿⡇⣼⣿⣿⡿⠀⠐⠌⣂⠡⢊⠐⡄ ⠠⢁⠒⡈⢄⠊⢄⢊⡐⢁⠂⠆⡁⠆⡨⠁⠎⢠⠂⡡⠌⢡⠐⣁⠂⠥⠘⢠⠁⠜⠠⢄⠩⢐⡈⢌⡐⢂⠁⠂⠀⡠⢼⠻⠿⣿⣿⣿⣷⣍⠂⢠⢉⡙⠒⠴⣀⢄⠢⢄⠠⡀⢀⠁⠐⠂⠰⠐⡈⠀⠀⡀⠈⠀⢠⠖⡤⣄⠀⡼⣩⢍⠯⣭⠹⣍⠯⣍⠏⠀⠀⠀⠀⢸⠀⠿⢋⢦⡀⠠⣛⢿⣿⣿⣿⡇⢸⢡⣿⣿⡿⠁⠠⣉⠰⠀⢆⠡⠌⡐ ⢀⠃⡌⢐⠂⡉⢄⠂⡄⠃⢌⢂⠡⢂⠡⡘⢈⠄⠢⢁⡘⣀⠒⢠⠘⢠⠉⡄⠊⢌⠒⠠⠊⢄⡐⢂⠐⠀⢀⣴⣿⣿⣶⡌⠀⠈⠙⠛⢿⡟⣸⣶⣦⣤⣉⡒⢄⠊⡔⡉⢆⠱⡈⠜⡰⢐⡠⢄⠀⠀⠀⠄⠁⠀⡜⠮⠑⢮⡱⢣⡓⣎⠳⣌⡳⣌⢳⡌⠀⠀⠀⠂⠀⢈⡽⢎⡝⣢⢁⣻⣶⣜⣿⣿⣿⡇⠀⣸⣿⠟⠀⢠⠡⠄⢂⠍⡠⠒⣈⠐ ⢀⠃⡄⠃⡌⠰⢈⠰⠠⡉⢄⠢⢁⢊⡐⠄⢃⠌⢡⠂⠔⡠⢘⡀⠎⡐⢂⠌⢡⠂⡌⠡⡑⠂⠐⠀⣠⠾⢿⣿⣿⣧⢹⣿⣶⡤⠀⠀⠀⠀⠉⠛⠛⠿⠿⣿⡿⣿⣿⣿⣾⣶⣷⣾⣶⣷⣾⡞⠀⠀⢈⠀⠀⢠⣍⠠⣔⢣⡝⣣⠝⣬⠳⣥⠳⣌⢳⠂⠀⠀⠠⠁⠀⡰⢎⡳⡜⠁⢶⣿⣿⣿⣿⣿⣿⣷⠀⣿⠛⠀⡐⠂⡔⡈⠆⢂⡁⢒⠠⡁ ⢀⠃⡄⢃⠰⢁⠊⠤⠑⡐⢂⠌⢂⠆⠰⣈⠢⠘⡠⠘⡐⠤⢁⡐⢂⠡⠌⡐⠢⡐⡈⠅⠀⠁⣠⣞⢰⣋⢖⡙⢿⣷⠀⢿⣿⣦⠄⣱⣄⠀⠀⢠⣀⣀⣀⣴⣶⣶⣶⣄⣀⣀⣲⣶⣶⣶⣾⠇⠀⠀⠂⠀⠀⣀⡈⠓⠈⠳⠜⢡⡛⡴⡋⠖⠹⢌⡳⠀⠀⢀⠡⠀⠀⡇⣏⠶⡉⣸⣾⣿⣿⣿⣿⣿⣿⣿⢠⠘⠀⠐⡠⢃⠰⠠⠑⡂⠌⠤⢁⠂ ⢀⠣⠄⢃⠌⢂⠩⠄⡃⢌⠰⢈⠢⠌⠡⢄⠢⠑⡄⢃⠌⡐⢂⠌⡄⢃⡘⠄⡱⠐⠈⠀⣠⣾⣿⣿⡆⢬⡂⠽⣀⠙⢷⡈⢿⣿⣿⣿⣿⣷⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠀⠀⠐⠀⠀⢠⢧⡹⢥⡓⠶⠀⢧⡙⠶⠁⢤⣀⣀⡀⠀⠀⢂⠠⠀⠀⡳⢌⣳⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⠀⠄⡃⠔⢂⠡⢊⠡⡐⣉⠰⠈⠆ ⠀⢆⠉⡄⢊⠄⠣⡐⢁⠆⡘⠄⢢⠉⠔⢂⠌⡡⠐⡌⢠⠑⡨⢐⠠⢡⠐⠌⠀⠀⢀⣼⣿⣿⣿⣿⣧⡌⢻⣷⣬⣱⣌⠳⠌⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠁⠉⠁⡤⢂⣿⡄⠀⠈⠀⠀⡜⢦⡙⢦⡹⠁⣸⢣⡝⠃⢐⡣⢞⡴⠃⠀⠈⡀⠄⠀⠘⠁⠉⠈⠃⠻⠿⠿⣿⣿⣿⣿⣿⡿⠁⠐⡨⠐⢌⠂⡅⠢⢡⠐⢄⠢⢉⠔
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⣠⣤⣴⣴⣶⣶⣶⣶⣶⣶⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⠃⠈⠉⢻⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠙⣿⠀⠀⠀⣿⡏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⣷⡀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣀⣈⣩⡶⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⠿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢯⡙⢮⢏⡳⡹⢌⡇⡚⡔⣣⠚⡔⢣⡚⡔⢣⡚⡔⢣⢚⡔⢣⠚⡔⢣⠚⡔⢣⢚⡔⢣⠚⡔⣣⠚⡔⢣⡚⡔⢣⡚⡔⣣⠚⣔⢣⠚⡔⣣⠚⣔⢣⠚⣔⢣⠚⣔⢣⠚⣔⢣⢚⡔⢣⡚⡔⢣⢚⡔⢣⡚⡔⣣⠚⣔⢣⠚⣔⢣⠚⣔⢣⠚⣔⢣⢚⡔⢣⡚⡔⢣⢚⡔⢣⡚⡔⢣⡚⡔⢣⢚⡔⢣⠚⣔⢣⠚⣔⢣⢚⡔⢣⡚⡔⢣⢚⡔⢣⠚⡔⣣⠚⡔⢣⡚⡔⢣⡚⡔⣣⠚⣔⢣⠎ ⢧⡙⢮⠜⡲⢍⡲⢥⡙⢦⢡⢋⠼⡱⢌⡱⢣⢜⡸⡑⣎⠜⣡⢋⡜⣡⢋⡜⣱⢊⡜⡡⢏⡜⡰⡙⡜⡱⢌⡱⢣⢜⡸⢰⡙⢤⡃⢏⡜⡰⢍⢆⡣⠝⡤⣃⠏⢦⡉⢞⡰⢃⠧⣘⠣⣜⠸⣡⢃⠮⡱⡘⢦⡡⢋⡴⢣⡙⢤⡃⢏⠦⣉⠞⡤⢃⡇⢎⡣⢜⡸⢡⣃⠮⡱⣘⠬⢣⢜⡸⢡⣃⢎⢣⢋⠦⣉⠞⡤⢃⡇⢎⡣⢜⡸⡑⢎⡜⣡⠫⠴⣡⢋⡜⡱⣌⠱⡣⢜⡸⢰⡙⢤⠓⣎ ⢧⡙⣎⢧⡹⢆⡳⢦⡙⢦⢣⢍⠶⡱⣊⠕⡣⢎⡱⠱⣌⠚⡥⢋⡜⣡⠓⡜⡡⠞⡬⠱⢎⠴⢣⡙⠴⣉⢎⡜⡱⢊⡴⢃⠮⡱⢌⡣⢜⡱⢎⠦⡙⡜⢢⠕⣪⠥⣙⠬⡒⡍⢎⠥⣓⠌⢧⡑⢮⠱⣡⠝⡢⠵⣉⠖⣡⢎⡱⢜⡱⢊⡕⢮⡘⢥⠚⡜⠴⢣⡑⠧⡜⢢⡕⢪⠱⣃⠎⡖⢣⠜⡬⢲⠩⢖⡩⢚⡌⠧⡜⢢⠝⡢⢕⡩⢎⡜⢢⢍⡣⢥⠓⡜⡱⢌⠳⣑⢣⠜⣥⢚⡬⢫⠔ ⢣⠝⣢⠓⡼⢡⠓⡦⠹⡌⢦⠩⢖⡱⢜⢪⠕⠮⡔⡫⣔⠫⡔⢫⠴⡡⢏⠼⡱⣙⠴⣋⠮⡱⢣⢍⡣⣍⠖⣬⠱⣍⠲⡩⠖⣥⢋⡴⢩⡒⣍⠲⣍⠼⣡⠞⣡⠞⡤⡓⢭⢜⡩⢖⡩⢎⢣⡚⢦⠹⣄⢛⠬⡓⡬⡚⢥⢎⢲⣉⠶⡩⢜⡢⢝⢢⠝⣌⠧⢣⡜⡱⢜⡡⢎⡥⠳⣌⠳⡌⢧⢚⡌⢧⡙⢦⠱⡣⢜⡱⢜⢣⡚⣱⠪⡜⢲⡘⢥⡊⡕⢪⠹⢴⡙⢬⠓⣜⠪⡜⡤⢣⠜⡥⢚ ⢣⡛⡔⡫⣜⠡⣏⢲⡙⡜⣆⠻⣘⡜⡌⣇⢺⠱⣘⡱⢌⡳⢌⣷⣿⣶⣭⠒⡵⢩⠖⣥⠣⢇⠧⡚⢴⠸⡜⡰⣍⠦⢳⢩⠞⡰⢣⠜⣣⢱⢊⡵⣘⠖⣡⠞⣡⠞⣰⡙⢬⢒⡱⢎⡜⢮⠱⣌⢇⡳⠜⣬⢃⠧⡣⢝⠲⣜⠲⡌⢶⡉⠶⣡⠏⡜⡼⣈⢎⠧⣘⢥⣋⡜⢦⠱⣋⠴⢣⡹⢜⠲⡜⢦⡙⣆⢫⠱⣍⠲⡍⢦⡹⢄⡳⣉⠧⣘⠦⣵⣾⣥⢏⠦⣙⠦⡛⣌⠳⡑⢮⠱⡚⣌⢣ ⢣⡓⡼⠱⣌⢳⡘⣆⢳⢸⠰⣹⠰⡚⡔⡣⢎⣱⣵⡼⣦⣽⣾⣿⣿⣿⣿⣽⣴⣧⣾⣤⣿⣬⣶⣭⣶⣧⣾⣵⣬⣮⡵⢮⡼⣥⠷⢮⡴⢧⠮⡴⢣⡞⡥⠾⣤⢯⡴⢭⢦⣧⣜⣲⣘⣆⣳⣌⣦⣱⣉⣦⣉⣖⣱⣊⣵⣈⣳⡼⢦⡽⢦⡵⢮⠵⣦⢭⠮⢶⠭⡶⢴⡼⢦⡽⣤⠯⣦⠵⡮⡵⡼⢦⡵⣬⠶⣭⢦⠷⣬⢧⡼⡼⡴⣥⣮⣵⣾⣿⣿⡿⣿⣾⣤⣣⠙⣆⢏⡙⢦⢋⡵⡘⠦ ⢣⠳⡜⢳⡘⢦⡑⡎⢎⠶⣉⠶⡱⢩⡒⡕⢪⣹⣷⣷⣷⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣾⣾⣷⣾⣶⣿⣾⣷⣾⣾⣷⣶⣷⣾⣶⣿⣿⡿⣯⠽⣾⣿⣹⣭⣟⣻⡝⣿⣏⠿⣯⣟⢿⣻⣷⣷⣾⣶⣾⣾⣾⣶⣾⣾⣶⣷⣾⣶⣾⣶⣶⣶⣷⣶⣿⣶⣷⣾⣶⣶⣷⣾⣶⣾⣾⣶⣾⣶⣷⣷⣶⣶⣷⣶⣾⣿⣶⣶⣶⣿⣧⡝⡰⢎⡱⢎⡱⡒⣍⢚ ⢣⠏⡜⣥⡙⢦⠱⡍⡞⡸⢤⠓⣍⢣⠜⣩⢒⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣏⣿⣹⣾⣽⣿⣿⣿⣿⣿⣿⣟⣾⣼⣏⣿⣿⣿⣿⡿⣿⣿⢿⣿⢿⣿⡿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡻⢡⢫⡔⢣⠵⣉⠦⣩ ⢣⡛⡜⣤⢋⢦⢋⡖⣹⠰⣃⢯⡘⡬⢣⡱⢊⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⢿⣿⣽⣿⣯⢿⡿⣟⣿⣿⣾⣾⣿⣿⣿⣿⣿⡯⠿⣿⣾⣓⢎⣾⡳⣖⣾⣣⣻⢞⣦⣿⣯⡿⣷⡿⣶⣿⣾⣿⣿⣽⣿⢿⣿⣯⣿⣿⣻⣿⣟⣾⣿⣾⣿⢿⣻⣿⢿⣽⣿⣿⣾⡿⣷⣿⣟⣷⣿⣿⣾⣿⣯⣿⣿⣽⣿⡿⣯⣿⣿⡷⣿⣿⡑⡲⢜⢣⠣⣍⠲⣡ ⢣⡓⡼⢰⢋⠦⡓⣜⢢⢓⠥⡲⢡⡓⡣⢜⡡⢾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣛⣳⠋⢽⣝⣿⠽⢺⢳⠬⣋⣭⡟⣿⣾⣟⣯⡹⣻⡯⣷⣽⢯⣿⢿⢽⣿⣺⣹⣿⢽⡿⣿⣿⢿⢽⣾⡿⣿⣯⢻⣿⣷⣿⡾⢿⡿⣞⣳⣾⡷⣺⣺⡮⠟⣛⣰⣷⡿⣿⣯⣿⣟⣷⣿⣻⣿⢿⣻⣿⣟⣿⣾⣟⣿⣿⣿⣻⣿⣟⣷⣿⣯⣿⣟⣯⣿⣿⢿⣿⣟⣿⣿⣹⣧⠣⡕⢎⡎⠵⣊⡕⠦ ⢣⠳⡜⢣⡍⢖⡍⢦⢋⡬⢣⡙⢥⢚⡱⢊⡴⢻⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣼⣿⣿⢾⣶⣿⢽⣽⣻⣹⢿⢿⣽⣿⣺⣾⢿⣶⣻⣶⡿⣿⣾⢿⣿⣟⣿⣷⡿⣿⢿⣟⣿⣷⡿⣟⣯⣿⣟⣿⡿⣿⣷⣿⡿⣷⣿⢿⣿⣻⣽⣿⢿⣻⣽⣾⣿⣟⣿⣽⣿⣿⣯⣿⣿⣽⡿⣿⣷⣿⢿⣯⣿⣿⣯⣿⢿⣻⣿⣯⣿⣿⡿⣿⣻⣿⣼⡯⡑⢎⡣⡜⢣⡕⣌⠳ ⢣⠏⣜⡱⢪⡱⢌⠧⣍⠲⢣⠹⣌⢣⠜⡥⢊⣵⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣷⣮⣷⣿⣯⣿⣿⣾⣶⣽⣾⣯⣿⣷⣿⣿⣽⣿⣷⣿⣿⣾⣿⣿⣿⣻⣿⣾⣟⣿⣟⣿⣾⣻⣿⣿⣷⣿⣟⣿⣽⣿⣻⣟⣯⣿⣿⣟⣟⣿⣞⣿⣛⣯⣷⣻⣯⣷⣻⣯⣟⣿⣞⣿⣻⣟⣷⣻⣟⣿⣻⣟⣿⣽⣻⣷⣿⣟⣿⣿⢬⠱⣩⢎⡱⠜⡥⢚⠤⣋ ⢣⡛⡤⢓⡣⡜⢪⡕⣪⠱⣋⠼⣄⠫⣜⠰⣋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢃⡳⡌⠶⣙⠲⣍⠲⣡ ⢣⡓⡜⡣⡕⢮⠱⡜⣢⢓⡜⠲⣌⠳⣌⠳⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡑⢎⡴⣉⠳⣌⠳⣌⠳⡰ ⢣⡝⢬⡱⢍⡲⣑⢣⡕⢎⡜⡱⣌⠳⣌⠳⡰⢌⡫⢝⡛⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⠲⡰⣍⠳⣌⠳⣌⢣⠱ ⢣⢎⡵⣘⠣⡕⣪⠱⡜⡬⢒⡱⣌⠳⣌⠣⡕⡣⡜⡜⡸⢡⠎⣜⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⣌⠣⣕⢪⠱⣌⠳⡌⡖⣩ ⡓⢮⠴⣉⢳⡸⡐⣏⢲⡑⢫⢔⢪⡱⢌⠳⣘⡱⣘⠲⣉⢇⡚⢤⢋⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⡿⠿⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⢻⠛⡟⣛⠻⡛⢟⡻⢛⣛⣛⣛⢛⡛⣛⠻⡙⣏⢛⠭⣙⡌⢏⡭⢍⡭⣉⢧⡙⣬⠱⣉⠖⡱⢂⡳⢌⠳⣌⠲⣍⢒⡣⡕⡚⢤ ⡙⢦⣋⠼⣑⠲⣑⠎⣖⠩⢖⢪⢱⡘⢎⡱⢆⠳⣌⠳⣘⠬⡜⣡⠎⡴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡛⢭⡑⢮⡰⢊⡬⢓⣌⠳⣡⠓⣤⢋⠿⣿⣿⣿⣿⣿⠟⣌⠳⡌⠶⡙⢼⡨⢓⡙⢦⠓⣍⠶⣈⢎⢣⡙⣌⠳⣑⠎⣎⠮⡱⡘⢎⡱⢎⠴⡩⢦⠱⡢⢝⡜⢬⠱⣋⠴⣋⠖⣡⠳⣌⠚⡴⢱⢩⢒ ⡙⠶⣈⢧⢃⡳⢡⠏⣬⠹⣌⢣⠣⡜⢥⠚⣌⠳⣌⠳⡘⣜⠸⣄⠫⡔⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⡉⢦⡙⢦⠱⣋⠴⣋⠴⢣⢅⡛⢤⢋⡜⣹⣿⣿⣿⢣⡙⡤⢣⡝⣡⠝⣢⠕⡫⢜⢢⠛⡤⢓⡜⣊⠦⡙⡤⢛⠤⣋⠴⢣⠱⣉⠖⡱⣊⠵⡑⢎⡱⣉⠶⣌⢣⠓⡬⢲⢡⠚⡥⢓⡌⢧⠱⡍⢦⢋ ⣍⢳⡑⣎⢣⠹⡌⡽⢤⢓⡬⢊⡵⢩⡒⡝⣌⠳⣌⢣⠝⣰⠣⣌⠳⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⠡⢎⣱⢸⢡⡓⢬⠒⡥⢎⠣⢎⡙⢆⡣⢜⠲⣿⣿⣿⢣⠜⣒⢣⡚⢤⣋⠴⡩⢖⡩⢎⡹⣐⠫⡔⢣⢣⡙⡔⢫⠜⣢⠹⣌⢣⠱⢎⡱⢌⠖⡹⢌⡱⣘⠲⣌⠲⡩⢜⡡⢎⢣⡙⢦⡙⣌⢳⠸⣡⠎ ⣌⢳⡘⢦⢋⡖⣩⠖⣣⠚⣔⠫⣔⢣⠚⣔⢪⢕⢪⢜⢪⡅⠳⣌⠣⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣹⣿⣿⣿⣿⣍⠖⣢⠓⢦⡙⢆⡫⡔⢫⠜⣡⠞⣡⠚⣌⢓⣿⣿⣿⢃⠮⡑⢦⡙⢦⡘⢆⡳⢌⡲⡑⣆⢣⢓⡜⢣⢆⠳⣘⢥⡚⢤⡓⣬⠒⡭⣒⡱⣊⢎⡕⣪⠱⣌⠳⣌⢣⢓⡥⣚⡌⣣⢚⢆⢳⡘⢆⡛⡤⢋ ⢬⡓⣜⠪⡵⡘⢴⡩⣒⠭⢢⠳⡘⢆⠏⢦⠓⣎⠼⣘⢲⡘⣣⢌⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡥⢻⣿⣿⣿⣿⡘⡤⢛⡤⢋⡖⡱⡜⢣⡚⢥⢪⡅⡫⢔⣹⣿⣿⣿⡍⠲⡍⡖⠭⢦⡙⢆⡓⠮⡔⢳⡘⢦⠓⡬⢓⢎⡱⢣⡒⢭⢒⡱⢆⢫⠔⡣⢖⡱⢊⡴⢃⡳⢌⠳⡌⠶⡡⢖⡡⠞⡤⢋⡜⢦⡙⡜⢲⢡⢋ ⢎⡵⢌⢳⡡⢝⠢⡵⢡⠏⡥⢋⠵⣉⠎⢧⡹⢤⠛⣤⠓⣜⡰⢊⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡟⢿⣿⣿⢟⡰⢋⡜⢣⠜⣡⢍⢣⠜⣣⠣⡜⣱⣽⣿⣿⣿⣿⣎⠧⡱⢩⡝⢢⠝⡬⠱⠭⡜⠥⢎⠥⢫⠜⡩⢦⡙⢦⠹⡌⢎⡱⢎⠥⣋⠵⣊⠼⡡⢎⠥⡓⢎⠵⡩⢎⡱⢣⠹⢬⠱⠭⡜⢢⠹⡌⢧⣉⢎ ⢎⡖⢭⡒⡭⢪⡱⢃⡏⣜⡡⢏⠎⣥⢛⢤⢣⢣⠫⣔⠹⣄⢣⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣷⣿⣿⣶⣷⣷⣾⣷⣾⣷⣾⣷⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⡧⢱⢃⡞⣡⢛⢬⡙⣕⢪⡙⣬⠹⣌⢭⡱⢆⡙⣆⠏⣜⢪⡑⢮⢱⡡⢇⡭⢒⡍⢮⢱⣉⠮⣱⠱⣉⢖⣩⢣⢃⣏⡱⣉⠧⣙⡜⡢⡕⢪ ⢎⡜⢦⢣⢳⢡⣚⢱⢪⡔⣱⢊⡓⢦⡙⢆⡣⢧⡙⣌⠳⣌⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡱⢬⠱⢬⡙⡻⠿⡿⢿⠿⡿⢿⠿⡿⢿⠿⡿⢿⠿⡿⢿⠿⡿⠿⠿⠿⠿⢿⠻⣟⢫⡑⢎⡴⢃⡞⢢⡓⡬⣒⡱⣂⠗⣌⢆⡓⣎⡱⢊⡞⡰⢃⢞⢢⣃⠞⡲⣘⢣⢜⣢⢓⡌⠶⣡⠓⣍⡒⢆⡓⡎⡴⡑⣎⢲⢡⣚⢱⡘⢥ ⠮⡜⣆⠫⢖⠣⡜⢆⢧⠸⡔⢣⡙⢦⡙⢎⡱⢆⡕⢪⠱⣌⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢬⡑⢎⠵⣂⠧⡱⢩⠜⣡⢋⡜⣡⢋⠼⣡⢋⡜⢥⢋⡜⣡⠫⡔⢫⡙⢎⠳⣌⠳⡌⢦⡙⠦⡜⡡⢞⡱⠸⡔⢥⠲⣑⠺⣌⠲⡱⢢⠕⡣⢎⡱⢍⠎⡖⠬⢎⡱⢎⠲⡜⢤⠓⡬⢓⢆⡛⢤⠹⣘⠲⡑⢦⠓⡜⢢⠇⡜⢦⡙⠦ ⢣⠳⣌⢝⣪⢱⠩⡎⢎⡱⣩⢣⡙⢦⡙⢎⡱⣊⠜⡥⢓⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢤⡙⡬⡓⣌⠶⣉⠧⡚⠥⣎⠲⣅⢎⠳⡤⢳⡘⢎⡲⢱⢌⠳⡜⢣⡜⢣⡓⣌⠳⡜⢢⡙⢦⠱⡩⢆⠧⡹⢌⡣⠝⣌⠳⣌⠣⡍⢇⠞⣡⠏⡜⡬⠹⢬⡙⢬⠱⢎⠵⢪⠥⢫⠜⡩⢦⠹⣌⢣⢍⢣⠝⡬⣙⠬⢣⢹⡘⢦⡙⡜ ⢣⢏⡴⢊⢦⢣⡹⢌⢧⡱⢢⡓⠼⣡⠞⡡⠞⡤⢫⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⢌⢣⡜⣡⠓⣌⠖⣡⠞⣡⢋⡴⢣⠜⣌⠳⣌⢣⢜⣡⢣⣃⢎⠳⣌⢣⢜⡡⠞⡤⡓⣍⢣⢜⠢⢏⡱⢪⡜⡡⢧⣑⢫⡌⢳⢌⣣⠹⣌⢣⣃⠞⣱⢸⢩⡒⣍⠎⣕⠫⣜⡡⢞⣡⢋⡕⣎⡱⡜⣌⠮⣑⢎⡱⣌⠳⣉⢦⡙⢦⡑⢎ ⢣⢞⡰⢋⢦⢣⠜⣣⢎⡒⢧⣘⢣⡕⢪⠱⣍⠲⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣉⠖⡸⡔⡍⢦⡙⣤⢋⡔⡣⣜⢡⠞⣌⠳⣌⡒⡎⣔⠣⡜⣌⠳⣌⢒⠎⡴⢋⡴⢱⡘⡆⣎⡙⢦⣑⢣⢜⡱⡒⡬⣒⡜⢣⢎⡔⡳⢌⡖⣘⡚⣤⠓⣆⠳⣌⡚⡔⣓⠦⣑⢎⢆⡳⣘⢤⡓⡜⢤⡓⣜⢢⠓⣌⢣⠓⢦⡙⢦⡙⢬ ⢣⠞⣬⠹⣘⠦⣙⢆⠮⣑⠮⡔⡣⡜⢣⠓⣌⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⠫⡔⡩⠕⡼⢌⢣⡜⢢⠇⡎⠵⡘⢦⠹⢤⠓⢦⠱⡚⢤⠳⡜⡰⢓⠬⢎⡚⠴⣋⠴⣃⠞⡔⢎⡜⠲⡌⢎⡲⢡⠧⡱⢒⢬⠣⢎⠴⡓⢬⠲⡑⠮⡔⢭⢒⠳⢤⢣⡙⢆⠳⡌⢎⠖⡱⡌⢦⠓⡬⢣⠜⣢⢣⢋⡜⢪⡙⢦⡙⢦⡙⠦ ⡍⡞⣰⢙⢦⢣⠱⢎⡇⡳⠜⡴⢓⣌⢣⠹⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠱⣌⠳⡌⡵⢋⡴⢋⠖⡬⢣⠞⣩⠣⡝⣌⢣⠍⡞⡡⢏⡱⢍⠶⣩⠱⡍⠮⠥⣍⠳⣌⠳⡌⢮⡙⢦⠩⢇⠽⣨⠱⢣⠎⡵⢩⠆⠯⣌⠣⡝⡌⠧⣍⠳⣌⠣⢎⡝⢢⢇⡹⢌⠧⡹⢬⠩⡕⠼⡡⢏⡜⡡⢏⠴⢣⠍⡼⢡⠝⣢⠙⢦⡙⡜ ⡜⣥⠓⡎⢮⡘⢭⠲⣍⠼⣉⠖⡣⢜⢢⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢇⡳⢌⢳⡘⣆⢫⢔⠫⡜⡌⣇⡚⢥⢣⡱⣊⡜⢪⡱⣉⢖⡡⢏⡲⢡⢳⡘⣍⠳⣌⠳⣌⠳⣌⢣⡜⢆⡛⣬⢚⢤⢫⡑⣎⡱⢣⡍⡳⢌⡣⠵⣉⠶⣡⢓⡬⣙⠬⣜⡡⢞⡰⢋⡖⣱⢊⡵⣉⠶⣉⠶⣘⡱⣊⡝⢢⣋⠴⣋⡜⣢⠛⢦⡑⢎ ⡜⣆⢫⢜⡣⡜⢪⡕⣎⢚⣌⢚⡱⢊⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢱⡘⢬⢣⢚⠤⡓⢎⡱⢚⡔⢦⡙⣆⠣⡖⣱⣘⢱⡒⡍⣆⡓⣎⢲⣉⢖⡱⢊⡕⣪⡑⢎⡱⣘⢲⡘⢎⡒⢦⣩⢒⡱⢚⡤⢃⣇⡚⣱⢊⢖⡙⣆⡓⣆⡓⢆⢳⡘⢦⡑⣎⡒⣇⡚⢤⢓⢆⡳⡘⣆⡓⢦⡑⣖⣘⠣⡜⡲⣡⢚⠴⣙⠦⣙⠬ ⡜⣆⠫⢆⡳⣘⢥⡚⡴⣉⢆⢣⢎⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢎⡱⢊⢎⠖⡹⢌⠶⡩⠜⢦⠱⣌⠳⡜⠴⡌⢖⡱⢎⠴⡱⢌⠶⣌⠲⢥⢋⡴⢡⠞⡡⢧⠱⢦⡙⢦⡙⢦⠒⡍⢖⠣⡜⢣⢆⡓⠦⣍⠲⣉⠦⡱⢆⡹⢜⠢⡝⢢⠕⢦⠱⢆⡹⢌⠞⡤⢣⠕⢦⡙⢦⠱⡒⢬⠣⠵⡑⠦⡍⠶⡑⢎⠦⣙ ⡜⡬⢓⢭⠲⢥⠲⢥⡓⠼⣈⢖⢪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡩⢜⡸⢰⢋⡜⢪⠕⣩⠖⣩⠹⣌⠳⣌⠳⣌⠳⡌⠧⡜⢬⠣⡝⢬⠲⢬⠹⡌⠮⡔⢫⠜⣱⢪⠱⢎⡜⢦⡙⢦⠫⡜⣩⠣⡍⢇⠎⡵⢩⠦⡹⢌⡣⠵⣉⠶⣉⠳⡸⢥⠫⢬⠹⢬⠱⢪⡙⢬⢣⡙⢦⠹⣌⠣⡝⠬⣍⢣⠍⢧⠹⢬⠹⣌⠳⡌ ⡜⣥⢋⠶⡩⢎⡱⢣⠝⡬⡑⢎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡳⡑⣎⢜⣡⢋⡜⡥⢚⢥⠚⡥⣓⡌⡳⢌⠳⣌⠳⣘⡱⣊⢇⡳⣘⠥⣋⢖⡩⣜⡱⢊⢧⡙⢆⣣⠹⣌⡜⣢⡙⢆⡳⣘⠥⣣⡙⣬⡙⡴⢃⡞⣡⢓⡬⢃⡳⢌⣣⡙⢆⡣⡝⣢⠛⣔⢫⡑⢮⡑⢦⡙⣆⢫⡔⢫⠜⣣⠜⣢⢛⣌⡓⢎⡱⣊⠵⣘ ⡜⢦⡩⢎⠵⣊⡕⣣⢫⠔⣍⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⠳⣰⠙⡴⢊⡴⢃⠞⡰⢋⣆⡛⠴⣡⢚⡱⢊⡳⢌⡳⣘⢔⢣⢎⠲⣡⠞⣰⢊⢖⣢⠱⣋⠦⣙⡒⢆⣓⢲⡘⣤⡙⣆⠳⣘⢲⢡⡚⢤⡓⡜⣱⢘⡔⣣⠜⣣⢚⡒⢦⡙⢆⡳⣘⡔⣋⢆⡳⣘⠦⣙⢆⠳⣌⢲⣘⢱⢚⠴⣉⠦⣃⢦⡙⡜⢲⡑⣎⠲ ⡜⣣⠜⡎⣕⠲⣌⡕⡎⠼⡰⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣎⡱⢡⢏⠲⣍⠲⣉⠮⡑⢧⠢⡝⠼⡐⢇⢎⠳⡘⢦⠱⢎⡜⡒⢮⠱⢥⠚⡥⢚⠆⠶⣉⠦⢣⢣⠜⡱⡌⠶⡑⢦⠱⣊⠵⡑⢮⠱⡌⠧⡜⡜⢤⢋⡴⢡⠞⡤⠳⡌⠧⡜⡱⢆⠧⡜⢢⠇⠶⡡⢞⡡⢎⠳⡌⠶⡘⡬⢚⡜⣌⠳⡌⢦⠓⡼⢡⠞⡤⢋ ⡜⡥⢚⡱⣌⠳⡔⢎⡜⢥⢓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⢄⡣⢇⡎⠳⣌⠣⡥⢣⠝⣢⠝⡬⢣⠹⣌⠮⡱⢍⡎⡝⢢⡜⠭⢆⢏⡬⠹⣌⢣⡍⠧⡍⢎⡥⢣⠭⡱⠜⡥⢋⡖⠭⡜⢬⡙⢦⠹⡌⢧⠱⢎⡥⢋⡴⢋⡜⢥⠓⣍⠳⢬⠱⢎⢲⡉⠧⡍⢧⡙⢦⠹⡌⠧⡍⢧⡙⢬⠣⡜⠴⣩⠜⡥⢫⠜⣡⠎⡵⣉ ⣜⡱⢍⡲⢥⠓⣬⠳⡜⣌⠎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠲⡱⣘⠲⣘⠳⣌⠣⡕⢫⢜⢢⣙⠲⣉⠳⣌⢲⡑⣣⢜⡸⣡⢎⡹⣌⢲⡘⡳⢌⡲⣘⢣⡚⢥⡚⢥⡓⣍⡚⢥⡋⣜⣡⢋⢦⡙⢆⡫⢜⣢⠛⣆⡚⢥⣊⢳⡘⢎⡹⣐⢫⡌⡝⢪⡱⣘⢣⡙⢦⡙⢆⡫⢜⡱⣊⡕⣪⢅⡛⣌⡓⢦⣙⢒⣣⠚⣥⢚⡱⢌ ⢦⡙⡬⢚⡴⢋⡔⣣⢓⢬⠚⡬⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢣⢓⡱⡌⢇⣣⢓⡌⢳⣘⠣⢎⡲⣌⠳⣡⢓⡜⢢⢓⡒⣎⢲⢡⢚⡔⣊⢆⡳⡑⣎⠱⡜⢢⡙⢦⡙⢦⡑⢦⡙⢦⠱⡒⢆⣋⠦⣙⢆⡓⡎⡔⡫⣔⢩⡒⣜⢢⡙⣆⠳⣘⢲⡘⣜⡱⢂⡓⡎⣜⢢⡙⢆⡓⢎⡲⢡⡚⣔⢊⡖⡱⢊⡖⣘⡒⢦⡙⣤⠓⡜⢬ ⢦⣙⠲⣍⢲⡉⢖⡱⢎⡲⣉⠖⡩⢆⡹⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢭⠸⣡⠚⡴⡙⢬⢒⡥⢚⠥⢎⠵⣃⠶⣌⠳⠴⡩⠜⡥⢣⠞⡤⢓⢎⡱⠜⡬⢆⠧⡱⢊⡵⢪⠕⣩⠦⡙⢦⡙⢦⡙⠦⢭⠱⡍⢦⠓⣬⠲⡱⢬⠱⡱⢌⠶⡱⢌⠶⡱⢌⠇⢧⠲⡱⢢⠕⡫⠴⣉⠦⡓⢬⢣⡙⢦⠱⢣⠵⡌⠮⠴⣉⠧⡜⣡⠎⡵⠸⢤⠛⡜⢢ ⠦⣍⠖⣥⠓⡬⢃⠧⡳⢔⠣⢞⡱⢊⠖⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢦⢓⠥⣛⠴⣉⢎⠮⡔⢫⠜⡪⠵⡌⠶⡌⢧⠹⢬⠹⡌⢇⠮⡱⢍⠎⡼⢩⡒⡍⡖⡍⢧⠸⣡⠞⣡⠎⡝⢦⡙⢦⠹⡌⢇⠧⡙⢦⠹⢤⠓⡭⢆⢏⡱⢍⠖⣩⠎⠶⣉⠎⡝⡬⢣⡱⢍⠮⡱⢍⡬⢣⠝⡬⢲⠩⢖⡩⢇⠞⡬⢩⢣⠍⡖⣩⠦⡹⢌⠽⡨⠝⣌⢣ ⠳⣌⠳⡌⣏⠴⣋⡜⣱⢊⡝⡢⢕⡩⢚⡻⠿⠿⢿⠿⢿⠿⡿⢿⢿⡿⣿⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠿⡛⣌⠣⢎⡱⢊⡖⡡⢞⡰⢩⡚⣌⠳⣑⠎⣕⡚⣌⡓⢎⡱⣊⢇⠳⣑⢎⡹⣐⢣⡱⢚⠴⡙⣆⢛⡤⢋⢦⡙⣜⢢⡙⢆⡳⣉⠞⡲⣙⣌⡓⢎⡹⣐⡋⣆⡓⣎⡹⢄⡛⣬⡑⢮⡑⣎⡱⢜⣊⢖⣩⢒⡥⢓⡚⣌⢣⡝⢢⡓⢎⡱⣊⢇⡣⢞⡱⣂⢳⡑⣎⢎⡱⢋⣆⢣ ⠳⣌⠧⣹⢰⢣⢒⡱⢆⡳⢌⡕⢎⡜⡱⢌⠳⣉⠦⡹⡸⢸⢡⢋⡖⢦⡑⠮⡴⢱⣊⠴⣂⠖⣔⢢⠖⣌⠣⡕⣪⢑⡣⢜⡱⢬⡑⢎⣒⢣⡱⢊⡵⢊⠞⡤⡓⢦⡙⡜⢲⢡⢎⠳⣘⠦⣑⢎⡱⢜⢣⡚⣱⡘⢲⣘⢣⠲⡑⣎⠲⣉⢖⡱⢊⡎⡕⣢⢒⣍⠲⣑⠦⡓⢆⡓⢦⢱⢊⡕⣢⡙⢆⡓⣆⠳⣘⠴⣊⢆⡣⢎⠳⣘⡔⢣⡜⢣⡜⢪⡱⡘⢦⢱⢊⠖⡱⢢⡓⣌⢲⣑⢣⠜⣢ ⡹⢆⠽⣐⢇⠎⣥⠓⠮⠴⡩⢜⠪⠴⣉⠮⣑⢣⢃⠧⣍⠣⣎⡱⣘⠦⣙⠲⣡⠧⣘⠲⣉⠞⣌⢦⠹⢤⢋⡴⢡⠣⣜⠸⡔⢣⡜⢥⢊⠶⡡⢏⠴⣋⢜⠲⡩⢦⠱⡍⢮⡑⢮⡑⢣⢎⡱⢎⠼⡘⢦⠱⢥⠚⡥⢎⠲⡍⠵⡌⢧⠩⢆⠧⡹⠰⡍⢦⠣⡌⢧⠱⢎⡱⢭⡘⢎⠦⣍⠲⡅⢮⠱⢎⠴⡙⢬⠲⢥⠚⡴⢩⠣⠵⡨⠧⡜⠥⢎⠵⡒⢭⠲⣉⠮⡩⢕⠣⡜⢬⠲⡌⢮⠱⢢ ⡱⢏⡞⡵⢮⠽⡠⢏⡍⢣⡙⢬⢩⠓⡬⢚⠤⡓⢎⠲⣌⠳⣄⠳⣌⠲⣡⢣⡑⢎⠴⣉⠦⡙⡔⢪⡑⢎⠲⣌⢣⠓⣌⠳⣌⠣⡜⢬⡉⡖⡩⢎⡜⡌⢎⡱⢥⢣⡙⡜⢢⡙⢦⡉⢇⢎⠴⣉⢎⡙⢦⡙⢬⡙⠴⣉⠳⣌⢣⡙⢬⡙⢬⢊⠵⡙⣌⢣⡙⡜⢬⡙⢬⡑⢦⡙⣌⠳⣌⢣⡙⢦⡙⣌⢣⠹⣌⡙⢆⢫⠜⣡⢋⠵⣡⢋⡜⡩⢎⡱⣉⢎⡱⣉⠖⡩⢎⡱⣉⢎⡱⢜⡡⢋⡥
gun text art /̵͇̿̿/’̿’̿ ̿ ̿̿ ̿̿ ̿̿💀💀💀💀💀💀💀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠉⠁⠀⠀⠀⠀⠈⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢠⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣖⣦⠀⠘⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠈⠛⠋⠀⡠⠐⠈⠁⠁⠀⠈⠉⠐⢬⠉⠀⠀⢣⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡒⠂⡀⠄⠠⠤⡐⢨⠟⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⢱⠀⠀ ⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣠⣤⣶⣾⣇⠀⠀⠀⣼⣿⣿⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀ ⢰⣿⣿⣿⣿⣯⣿⣶⣾⠿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠻⡻⣯⠯⡟⠚⠹⡻⣶⡿⠟⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀ ⠀⠀⠉⠀⠀⠀⠀⠀⠱⡍⠀⠀⠀⠻⠜⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡒⢒⡒⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣛⣦⡑⣤⣀⣀⣀⣀⣀⣤⣤⡔⠒⠋⠉⠉⠛⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠛⠋⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡶⠷⢶⡾⠿⠿⠿⠿⠿⠿⡿⠶⠶⠶⢶⢶⠦⠤⠤⠤⠤⠤⠤⠤⢄⡀ ⢠⡤⣤⢤⣤⣶⣶⣶⣲⣶⣶⣶⣶⣲⣶⢿⢸⠙⠒⡶⢲⢦⠖⠖⡾⡶⣶⠗⢶⣖⣶⠖⠒⠒⠒⢠⣶⣶⣶⣶⣶⢶⡾⠿⡿⡛⣿⠿⠿⠿⠍⠉⠉⠉⣩⡍⣻⡇ ⠈⠉⠀⠉⠉⠛⠛⣛⣿⠛⣛⡛⣿⣿⣿⣾⣼⡧⣴⣦⣤⣧⣠⣦⣭⣦⣤⣴⣿⣿⣿⣟⣫⣿⣽⣽⡟⠞⠈⠛⢃⣾⣷⢾⣾⡷⣶⣦⣼⣽⣽⣷⣤⡿⣿⢿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿⠿⡿⣿⣿⣿⣶⣶⣶⣶⣷⣊⣁⣠⣌⣉⣉⣿⡼⢹⣗⡀⠀⠀⣤⣼⡟⠀⠸⣟⣾⢏⠀⠀⠀⠀⢸⠋⣯⠿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⢸⣿⣿⣶⣶⣶⢻⣿⣿⠟⠉⠉⠎⢹⡦⣀⢀⣠⣦⣷⡿⠟⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣾⣿⡿⠀⠀⠀⠈⢆⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣷⣿⠇⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠘⢿⣦⣄⡀⠀⠀⢀⡇⠀⣼⣿⣿⣧⡶⢁⣴⣿⣟⡁⢀⣠⣬⣿⣿⢿⣿⣿⣦⣤⣀⣀⠀⢀⠀⠂⠀⡀⠀⠀⢀⣿⣿⡿⢁⣱⠀⠀⠀⠀⡹⠉⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠀⠀⠀⣈⣍⣥⠾⠚⢿⣿⣿⡿⠿⠿⣤⣶⣾⠟⣛⣋⡭⢿⢻⣾⣟⣧⣿⡿⠿⠋⢉⣁⣤⣤⣴⣶⣿⣽⣿⡿⣿⣿⡏⢰⣿⣤⡶⠛⠻⠷⣤⣧⠀⠠⣶⣾⠏⠀⠀⠀⢀⣳⣾⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⣮⣛⠿⢷⣦⣎⡀⣸⣿⢷⣿⠁⢠⣾⡿⠋⠀⠠⠾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣷⣶⡇⠀⠀⠁⣸⣿⣿⠟⠛⢛⠓⠀⢀⡜⠁⠈⢫⣿⣿⣿⣿⣿⣿⣿⣤⣶⡖⠚⣋⣁⣤⣶⣶⣬⣿⣿⣿⣧⠤⠄⠐⢯⣥⡟⠁⠀⠀⢘⡴⢿⣾⣻⣵⣶⡶⠿⠟⠿⠷⣅⠙⢛⣛⠿⠯⡿⢿⣯⡿⣿⣿⣿⣷⣾⢻⡟⣿⣷⣄⣀⣉⣄⣤⠴⢲⣚⣽⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡟⠉⠁⣟⣷⡷⣂⠈⠉⠻⠿⣴⣿⣔⣻⠟⠳⠀⣔⢛⣿⣿⣿⣿⣿⡿⢷⣿⡿⠋⡀⠠⢲⠆⠀⠀⠑⢠⠀⠀⠉⢿⣟⣀⣀⡄⠀⢠⡋⠀⢀⡤⠻⣇⡀⠛⢿⣻⡋⢻⣧⠘⠿⡉⢉⣁⣿⠿⠿⠋⣿⡛⠻⣿⡠⠴⠖⠚⠉⠉⣁⣠⣤⢨⣀⣾⡽⢿⣿⡅⡷⠤⢀⠀⢠⡏⢉⡇⣐⣴⣶⣧⡾⠀⠉⣿⡁⢹⢦⡟⢸⡇⣿⡿⢟⣯⣽⣿⣿⣻⣭⣿⢿⣿⣿⣿⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡠⣾⡇⠀⠀⠀⠬⡷⠄⢿⣶⣦⣄⡸⠿⣌⠉⠀⠀⡮⣉⣿⣿⣿⣿⣿⠋⠀⢸⣿⠁⠘⠀⡴⣋⡄⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠦⠀⢏⣀⣰⣻⠄⠀⠀⢁⣷⠀⢻⣧⡀⠉⠉⠀⠘⢄⠀⢸⣿⡷⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣏⠻⣧⣘⣿⢿⡾⣄⣀⡵⢾⠀⢘⣾⣫⣶⣮⣽⡇⠀⢐⣇⣇⣾⣭⣧⡼⠧⢛⣇⣌⣹⣿⣿⣿⡿⣿⣿⣿⡏⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠈⠛⠭⣛⠒⠦⣄⣿⣿⡟⣿⣿⣿⣿⣾⣷⣶⡾⠚⠉⠻⢿⣿⣿⣿⠀⠈⢸⣿⠀⠀⣶⣻⣿⡇⠘⠀⠀⠀⠀⠀⢀⡏⠀⣴⠀⠀⠀⠀⠸⡄⠀⠘⣿⣷⠃⡀⠀⢨⣿⣿⠭⣿⣷⡀⢀⣠⣤⣼⢷⣿⣽⣧⠤⢴⠖⢻⣿⠛⣛⣉⣭⣤⣿⣿⣿⣤⣿⡗⠚⠚⠋⠁⠀⠀⡸⢶⠶⠿⠛⠉⣻⣇⠀⣄⣿⣭⣿⠿⡟⣰⣿⣿⣍⡉⠙⢿⣿⢿⣷⡶⠾⠛⠈⠃⠈⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠻⣆⠀⠈⠛⠢⠭⣌⡡⠾⠟⢿⣿⣿⡛⢿⣿⣦⡄⠀⠀⠙⠻⣾⡀⠠⠈⢻⣆⢠⡉⠉⠛⣣⠞⠀⠀⠀⠀⠀⢸⡇⢀⡇⠀⠀⠀⠀⡴⠁⣠⠟⠙⠿⠉⠀⣠⡾⡻⠻⣯⠙⣿⣿⣿⣟⣯⣿⣿⣿⡿⠛⣢⠈⣧⡀⣻⣻⣿⠿⠝⠻⡋⠉⠉⠣⣀⣠⣤⣤⡤⠤⠔⡛⡐⠈⢀⣀⣴⣾⣟⣸⣛⣻⡿⣏⣿⣠⡛⠿⠿⠿⠍⠉⠉⢹⣿⢀⣿⡿⣶⣷⡄⠁⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠀⠸⡇⠀⠀⠀⢀⠈⢻⣷⣷⡈⠉⠻⣇⠀⢿⣿⣿⣶⣄⠀⠀⣨⣿⠶⢤⡀⢹⣄⡉⠀⠘⢠⠆⠀⠀⠀⠀⠀⣼⠁⣸⠇⠀⠀⠀⣀⣵⣾⣅⡀⠀⣈⣶⣾⣿⡟⠃⣁⣼⣶⣿⣿⣿⣿⣯⣿⣿⣛⣟⣿⣿⠛⠋⠉⠉⠀⣀⣀⣤⡴⠧⠖⢒⣋⣉⣹⣿⣿⣦⣠⣽⣺⡿⣿⣟⣉⣻⠟⢧⣸⣸⣾⣿⡽⢿⠟⣿⣿⣿⣶⣾⣶⣿⣿⠿⣏⠉⠀⣼⣇⣹⣦⡠⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢣⡈⠢⡀⠁⠀⠀⠀⠠⠤⠼⠿⢿⡿⠤⣘⣿⠀⠀⠻⣿⣟⡟⣷⣼⠟⣡⣾⣶⣝⣿⣿⣿⣷⣶⣋⣀⣀⣀⣀⣀⣶⠿⠿⠿⠖⠒⠒⠋⠁⠈⢿⡇⢀⣴⣿⠟⠉⣀⣤⡾⢋⠴⣿⢛⣵⣿⣿⡿⠿⢝⣿⣶⡇⠀⢢⣴⢶⠞⠛⠉⠉⠀⠀⠀⢠⠃⢈⣧⣸⠧⠖⠛⠋⠉⠀⠀⠀⠈⣿⣍⣀⣀⣀⣀⣛⡿⣿⣿⡿⠟⠉⢹⣿⢻⣿⣿⠿⠦⠾⠤⣦⣬⣿⣿⣿⣷⣾⡁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢣⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⠀⢸⣿⣶⡈⢻⣾⣿⢟⣵⣿⣿⣿⣿⣿⣿⣟⠻⠍⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡿⠟⢇⣠⣾⢛⣽⣶⣣⣴⣿⣿⣿⡿⢿⣤⠾⠿⣿⣿⣷⣰⡸⣿⡏⡋⠀⠀⠀⠀⠀⣀⡘⣄⡈⠿⠿⠂⠀⠀⠀⠀⠀⢠⣤⣴⣿⣮⡿⠿⠷⠶⠿⣦⣿⠁⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⡖⠀⠀⠉⢿⣭⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢃⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣠⠶⠛⠉⠳⣿⣿⣿⣿⣯⣭⠿⡿⠃⠀⢳⣏⣿⣿⡞⢹⣧⠁⠛⢧⡇⠀⢀⣀⡠⢊⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⣼⠛⣿⠀⢴⠀⠀⠀⢸⣿⣃⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣏⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠈⢆⣠⣤⣤⣤⣴⣶⣶⣶⠦⠤⠤⠄⠀⠈⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣰⣿⣿⣿⣫⣭⣿⢣⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡴⠾⣶⣭⣤⢶⣶⣿⢿⣿⠙⣿⣿⣿⠏⠀⠄⠀⣀⣾⣿⠉⢹⣴⣋⣿⣄⡤⠤⣷⠆⢉⠌⢠⣾⡇⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣸⡇⣀⡉⠀⠀⠀⣞⣿⣿⡄⠀⠀⣿⣿⢿⡄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⢿⡛⢆⠙⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠼⠿⠿⠟⠛⠿⠍⢍⣠⣤⣬⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⡈⠉⠉⠻⣿⣿⣿⣼⣤⣤⣦⡖⢉⣿⡟⠋⣭⣴⣃⣀⣴⣿⣦⣶⣯⣾⡇⣤⣸⣿⣿⣿⠁⣀⠀⠀⠀⣽⣿⠇⡠⠴⢿⣾⣯⠉⢺⡿⢹⡠⠂⣴⠿⢿⣇⣹⢹⠀⠀⠠⡀⠀⠀⢀⣶⠟⠋⠉⠉⠉⠙⣿⣉⡓⠲⢴⣿⣜⣯⣳⠀⣴⣿⣿⣍⡀⠀⠀⠀⠀⠁⠀⠀⠀⡠⠀⠀⠘⢷⣀⡇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣤⢸⢷⡾⣶⣤⣦⣀⡀⠀⠀⠀⠀⠙⠓⠛⠳⣦⣶⣴⣶⡤⢄⣠⡞⡀⢀⠐⡀⠀⠀⢹⣯⢻⡿⠟⠻⣿⣷⠾⢿⣇⣼⠉⢰⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣷⣿⣿⣿⠄⠀⠁⣰⣾⣿⣾⣾⣤⡤⠚⠛⠛⠷⣾⢉⣻⣤⣼⠋⠈⢸⣿⣿⠸⠀⠀⡴⣃⣴⡾⣿⣿⣷⢦⡀⠀⠀⠀⣿⡬⠟⠗⠚⠿⣿⣿⢿⣯⡛⣿⡿⠉⠀⠀⠀⠀⠇⠀⢀⡄⠀⠀⠀⠀⠀⠙⣧⡠⠄⢐⡄⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡣⠃⠀⠀⠈⠓⠘⠋⠙⠛⠿⢷⣤⣄⠐⠄⡆⠁⠉⠙⠛⠃⠀⠋⠁⠑⡀⠁⢣⠀⠀⠈⣿⣼⣿⣶⣷⣾⣯⠀⢸⣿⣿⡀⢸⣏⣿⣿⠿⣿⣿⣿⣿⣇⢀⣽⣿⣿⣿⠀⠀⣸⣿⠿⠞⠋⠉⠀⠀⠀⠀⠀⣀⣿⣿⠉⣿⠀⠀⠀⢰⢹⢻⢸⣂⠜⢑⣿⣿⣻⣿⣵⣿⡇⣿⣄⢀⢀⣿⡇⠀⠀⠀⠀⠘⠻⣴⡏⢳⣼⣀⡀⠀⠀⠀⠰⠀⠀⡇⠀⢀⠀⠀⠀⠁⠀⢿⣶⠻⡿⡃⠀⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⠊⠀⠀⠉⠠⣄⣿⡟⠻⡏⢱⣀⣿⣄⣼⠟⡟⢻⣏⣯⣿⣶⣾⣫⣽⣿⣿⠋⢁⣾⣿⠉⡿⠀⠂⠉⠀⠀⠀⠀⢀⠀⢠⣤⣞⣟⣻⣿⣿⠀⣾⡀⠒⠀⠀⢿⢸⣼⣧⠚⠉⣿⣿⣻⣿⣿⣿⣷⣿⣿⣄⠘⡆⢹⣤⠔⠒⠒⠂⠀⠙⣧⣼⡇⠉⣿⡀⠀⠁⠲⠃⡐⠁⠀⣸⠀⠀⢠⣇⠀⠀⣿⣿⠿⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢰⣆⡀⠀⠀⠈⠑⠀⠀⠀⠀⡠⠈⠀⣀⣤⡶⠦⣀⠈⠿⣧⠼⣷⣿⢯⠏⣹⣸⡆⣧⣿⣿⣿⠟⠟⠋⠉⠀⠀⢠⢤⠟⠋⡿⣸⠃⠀⠀⠀⠀⠀⠀⠒⠉⠀⠟⠙⡠⢻⣿⣿⣿⠀⣿⡇⠀⠈⣃⣸⣼⣏⠙⢶⣴⣿⣮⣽⡟⣿⣿⣿⣿⠋⠛⣦⣿⠛⣧⢧⡄⠀⠀⡄⠀⠘⣧⠑⣰⠟⠇⠐⡀⠀⠀⠇⠈⠂⢸⠀⠀⠀⣸⡀⠀⠙⣷⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠉⠈⠐⠹⣿⠉⠐⠿⠅⠀⠈⠉⠉⠀⠨⠄⠠⠆⠀⠀⠀⡠⠊⠀⠀⠀⠡⢰⣍⣁⠶⠧⠀⠰⡠⣹⣿⣸⠘⢿⠃⣇⣿⣘⡾⠃⠀⠀⠀⡀⠀⠀⣾⡿⠀⣸⢧⠃⠀⠀⠀⣠⠤⡤⠀⠀⠀⡰⠂⡜⠀⡏⣿⣿⣿⡄⡿⠁⠀⠀⣧⣽⡿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠀⠀⣿⢻⣧⠻⣆⢳⠅⠄⠀⠀⠀⠹⣘⠣⢤⣜⣷⠈⢶⡂⠀⠀⠀⠠⠀⠀⠀⡭⠠⠀⠀⢸⢟⣉⣥⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠀⡀⡀⠑⠳⠶⠤⣉⡀⠀⢀⠴⠶⣿⡚⠓⠒⣤⡄⠐⡦⢡⣖⠀⢐⣮⣖⣤⠔⠒⢿⣿⠀⠀⠁⠀⠐⢘⣛⡻⢇⣼⣿⣿⣿⠋⠀⠀⠀⠀⠙⠃⠛⢲⣿⣇⡀⣿⡞⠀⠀⠀⠀⠀⠀⠀⢀⡀⣴⠖⠈⣀⡞⠁⢻⣿⣿⡇⠇⢀⡠⠞⢋⣡⢴⡾⠿⠿⠿⠿⣿⣿⣿⡿⠟⠋⠁⠀⠀⣿⣸⣿⠀⣹⣆⠀⠀⠀⠀⠀⠀⠸⡍⠐⢿⣿⡵⠀⣱⢀⠀⠀⠀⠆⠀⠀⡇⢠⠤⠴⠿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣧⠘⠥⠤⠤⠔⠂⣴⡄⢹⢿⠀⠀⠀⠀⠀⠉⠉⠛⢦⢴⡋⣩⠽⡟⢿⠟⠀⠀⠀⠀⠈⠁⠀⠐⠄⠠⡀⠻⣿⣶⣤⣉⠛⠁⠀⠂⠀⠀⠈⠀⠀⠀⢈⢹⣷⣷⡿⠁⠀⠀⠀⠀⠀⠀⢐⠃⣠⠏⢀⡴⠋⠧⣴⣿⣛⣍⣧⡗⣡⣴⣾⣿⣿⡿⠃⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⠀⠒⡿⢧⢆⠀⠀⠀⠀⠀⠀⢹⣆⠉⣿⣟⡵⣯⡤⡡⠀⠀⠀⡤⠀⡹⢃⣤⡖⢊⡔⠀⢀⠞⠉⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣧⠀⢤⠤⠖⠾⣄⣾⠋⠉⠹⠤⣀⠀⠀⠀⢀⣤⡿⠣⡀⠀⠀⠈⠉⠀⠀⠀⠊⢵⣄⠀⠀⠀⠇⠀⠻⣄⠘⢿⠮⡙⢿⢷⣶⣄⡀⠂⠀⡀⠀⠀⢈⠹⣿⣿⠃⠀⠀⠀⠀⠀⠀⢠⠆⠠⠃⢠⠟⠀⠀⣰⣿⣿⡟⠿⠉⢹⣌⠛⣿⠟⠉⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⠀⢠⠃⠀⠀⣿⣿⣾⡂⡷⠈⢎⣀⡀⠀⣀⡀⠀⢀⠻⣆⣰⣏⣿⣿⣗⣇⢱⣶⠀⣡⡎⣀⠜⠋⣀⡈⠀⡆⠁⣄⡠⢊⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⡆⠀⢑⣶⡤⣈⠙⣶⠃⡈⠑⠛⠲⣆⣴⣮⠿⠃⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⡷⠋⠘⢶⣌⠣⡈⠶⣻⣿⣿⣃⠀⠀⠀⡀⢄⡎⠰⣿⠃⠀⠀⠀⠀⠀⠀⢠⠏⠀⢣⣴⠋⠀⠀⠀⣿⣿⣿⣿⢄⠀⠀⣉⠗⠁⠀⠀⠀⠀⠀⡇⠐⢺⣿⣿⣿⣿⡀⢸⠀⡀⠀⣿⣻⠈⡧⣸⠀⠘⡅⡨⠊⠁⠀⠀⠀⠀⠻⣧⣘⢻⣿⣿⡿⠊⢹⣧⡀⠀⠠⠶⠛⡡⢃⢢⠸⣞⡡⠖⠛⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣷⡤⠈⢧⡀⠀⠀⠉⠀⠀⠀⠏⡑⠛⢿⠛⠀⠀⠐⠀⠈⠄⠀⢤⣀⣠⡄⣄⣀⣤⣠⣿⣿⣶⠃⠀⠀⠈⠻⣷⣰⡶⠿⣽⡗⠚⠀⢄⣸⣧⢤⠗⠙⠇⠀⠀⠀⠀⠀⠀⠀⡜⠀⣸⣿⠁⠀⠀⠀⣰⣿⣿⣿⣿⣾⣿⣿⣿⠄⠀⠠⠀⠰⠀⢤⠁⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠴⣿⣟⣿⠃⣴⠀⡄⢹⠀⠀⠀⠀⠀⠀⠀⠀⢈⢫⡹⠿⠿⠟⠋⠉⠀⡛⣮⡁⠤⠐⢁⠁⢐⣊⠁⠀⡆⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣿⣧⠀⠀⠀⢀⣀⡀⠀⣄⣠⡎⠀⠀⠀⠀⠀⡀⠠⣀⣀⠚⢄⡶⠦⠽⣷⣿⣽⣿⡯⣿⣿⣿⣿⣦⡀⡄⠀⣨⣏⣿⡀⠢⠗⠠⠴⢍⡉⠋⠊⠁⢸⠠⠄⡀⣀⡀⠀⠀⠘⠁⢠⡏⡸⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠒⠀⠀⡆⠀⡈⣿⣿⣿⣿⣧⠀⠀⠀⠀⣿⣋⣏⠉⢿⣃⠁⠤⢷⠀⠀⠔⠂⠀⠐⢤⡈⠀⠙⢖⠆⠀⠀⠀⠀⣸⢋⡿⡆⠠⢻⠀⡿⠟⠀⠘⠣⡈⠄⠀⠀⠀⠀⠀⠀⢀⠅⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠀⠙⠳⠆⠀⠀⠰⠂⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⠀⠐⢶⠛⢅⣀⠙⣿⡳⠀⠀⠀⠀⠀⢰⠟⠛⠀⠚⡲⠚⠗⠀⢰⣴⣿⣟⠛⠒⠟⠏⠈⠙⠿⣿⣦⣨⣼⣽⡿⣷⣄⠁⠀⠀⠲⡄⢀⡒⢠⣁⠄⣠⡔⢸⣄⣷⠪⣲⡀⠈⣠⠇⢀⣴⣿⣿⡿⠿⠟⣿⣿⣋⣤⣶⠤⠀⠀⠀⠀⠐⠀⢰⠀⢆⠑⢿⣿⣿⣿⣿⠀⠀⠒⠠⣿⠀⢿⠀⢸⡇⣰⣦⢊⢧⡀⠀⠀⢀⣀⣀⡈⢴⠒⠈⢻⣦⣤⡤⢞⡽⠀⡧⣣⠀⠀⠀⠀⠀⠀⠀⠀⢤⠰⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣠⣰⣥⠀⠀⠀⠀⠀⠀⠐⠤⡄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡿⠄⡠⠚⠀⠐⢄⣜⠁⠀⠐⢦⠀⠤⠴⠉⠐⢄⠀⠀⢰⡄⠈⢄⣼⠛⠓⠇⢤⣀⡄⠀⠀⣤⣤⡻⠻⣄⠙⢿⣿⣿⣿⡀⠀⠀⢀⡈⠂⣘⠾⠧⠄⠀⠿⠂⠀⠀⠷⠏⣏⢫⣭⣶⡿⠛⠉⠀⢀⣤⡾⢋⡩⠿⠋⠁⠀⠀⠀⠀⠀⠀⠉⢾⡀⠀⠀⠸⣿⣿⣿⣿⡆⠀⠀⠀⡟⠀⣸⢀⡃⠈⢠⡋⡌⠘⢗⡤⠎⠁⠀⠀⠠⠀⠡⠄⢸⡌⢢⡈⣓⣷⡿⣓⣿⣧⣖⠀⠀⠰⠾⠇⠀⠈⠢⠑⡀⠀⠀⠀⠘⠀⠀⢠⠀⢀⠀⡄⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠠⠀⠀⠀⠀⠁⠹⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠰⢀⠎⠀⠯⢿⠦⡜⣷⡀⠀⠀⠀⠀⣀⠀⠀⢧⠀⠘⡟⠋⠀⠀⠘⢿⣅⠀⢠⣾⡷⡀⠀⠙⢷⣌⣿⣿⣿⣵⡆⢀⠉⠈⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣦⣿⠿⢋⣽⣿⡿⣿⣿⣷⠚⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢿⣿⣿⣿⣇⠐⠀⠀⣯⣿⣽⣛⡂⢀⠈⠸⠀⠉⡿⣅⠔⠒⠀⠀⠐⠢⢀⠁⠘⡗⠈⠻⣯⣤⣶⣿⣿⣧⣾⣆⠄⠀⠀⠀⠀⡄⠐⠧⠁⣀⣀⡀⢄⢴⡌⠢⡑⠍⡅⠁⢀⠀⢈⣀⠀⡄⢀⠀⠀⡀⠀⠆⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⢂⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠟⡃⣀⢢⣼⣓⡞⠀⠀⠀⡰⠀⢇⠘⣿⠀⠀⠀⠀⠈⠲⠤⡈⡆⠀⢘⣄⣤⠀⠀⣸⣿⣖⢾⣿⣿⡿⠀⠀⠈⢏⣷⣏⢉⢹⠙⠂⡝⢃⠃⠀⠀⠀⠀⠀⠀⠀⠘⣄⣦⠖⢦⠸⡽⣿⣿⣷⠙⠀⠐⠨⡀⠀⣀⣤⠤⠖⢂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠟⢻⡧⡽⠀⠀⣧⣤⣬⣧⡼⠂⠀⢀⠔⠊⠀⢳⡀⠀⠀⠀⠀⠀⠀⠑⠒⡟⠀⠀⠈⠻⣦⣿⡿⢛⣯⣹⣧⡀⠀⠀⠈⢀⢠⠀⠡⠙⡏⠀⠈⠿⠃⡈⠀⡐⡄⠒⠘⡄⠸⣄⠀⣅⣸⡀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢨⠀⠀⢀⠀⠫⣽⡞⠀⢴⣦⣤⣍⢐⠉⣭⠿⡄⠀⠀⠀⠀⠀⠀⠀⢘⠀⢻⣷⡜⠶⠚⡟⠁⣾⣿⡟⢅⣄⣼⡤⠄⣀⠳⡏⠀⢺⠳⠤⣈⠉⠀⠄⠀⡀⠀⠀⠀⠀⠀⠤⡈⠑⢼⠦⠀⢘⢿⣿⣏⠁⠀⠤⠘⠀⢸⠟⠩⠀⢌⠁⠀⠀⠀⠠⠀⠂⠀⢀⠠⠀⠀⣷⣾⣿⠛⠃⠀⠀⡗⠮⣿⣏⡃⠀⠈⠀⠁⡀⠄⢈⠡⠀⠀⠀⠀⠀⡀⠀⠘⡃⠀⠀⠀⠀⠀⠙⢦⠀⢉⣿⠿⣷⡞⠀⠐⢟⠟⢡⠄⢧⡈⠁⠀⠂⠈⠁⠈⠁⡀⢼⡆⡋⠀⡨⠁⠈⠈⠉⠁⠈⠁⠀⠀⠀⠀⡠⠶⠂⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣿⢻⣿⣯⣿⣷⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣯⣿⣟⣿⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⣿⣿⣿⡿⢿⡿⠋⣽⣻⣀⣀⣀⣠⠤⠤⠤⠼⠿⠿⠀⣰⣿⠋⢨⣿⠟⢿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⣋⣹⣿⠴⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠼⣿⣿⣧⣶⠉⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠾⠛⠉⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣦⣦⣤⣴⣶⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠈⣿⣿⣤⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⡇⠀⣀⣤⣴⣶⣿⣿⣿⡟⠋⢹⡏⣿⣿⣿⡟⣿⢻⣅⣸⡧⠶⠚⠉⢹⠙⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠛⢻⣿⣿⣿⢹⣿⡟⣿⠓⠲⢾⣿⣿⣿⢸⡇⣿⢺⡏⢹⣧⣤⣤⣤⣸⡇⣿⣿⣿⣹⣿⡟⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⢿⣿⣿⢸⡟⡇⣿⣠⣴⢿⣿⠃⣿⣼⣧⣿⣼⣇⡼⢋⣡⣤⣄⡉⠻⣿⣿⣿⡿⣿⣧⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠃⢸⣿⣿⣾⣧⣿⠋⢀⠴⠢⣌⠻⣿⣿⢿⣿⣿⡏⢡⠎⢁⣀⠈⢻⡄⠙⣿⣿⣇⢹⣿⣿⣿⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⢠⠏⢠⣦⡌⡇⢼⣿⢸⣿⣿⡇⠘⣄⠘⢛⢁⣈⡇⠀⢹⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣇⢸⣤⡀⣀⣠⠏⠘⠇⠸⠃⠸⠇⠀⠘⠻⠼⠶⠟⠁⠀⠈⢹⣿⡇⠀⠉⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠃⠘⢿⣏⢡⡀⠙⠋⢉⣁⡴⠆⠀⢀⠀⠀⠀⠀⠙⠶⠤⠤⠤⠶⠃⠀⠈⢟⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡀⠀⠈⢹⣆⣈⣽⣿⠉⠁⠀⣀⣠⡤⠴⠒⠒⢿⣿⣧⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠳⣄⠀⠘⣿⡝⣿⢹⡄⠸⡿⠁⠀⠀⠀⠀⠀⠈⠁⠘⡆⠀⠀⠀⢀⣴⣇⣀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⢿⣇⣶⡾⡇⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⠻⢿⣿⡀⠘⡆⠀⠀⠀⠀⠀⠀⠀⢀⣻⣴⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠈⠙⠲⣿⣦⣤⣤⣠⣤⣴⡾⢛⡿⠟⠓⢺⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣶⣶⠶⣛⣽⠟⠋⣽⡏⠀⠀⣰⣾⣅⠈⠙⢿⣿⡯⠖⠋⠀⠀⠀⣰⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣠⣴⣿⣿⡿⠿⠟⠁⣠⡾⠁⡇⢀⣼⣿⣷⡈⠓⠲⠾⣿⠳⣄⠀⠀⢀⣴⣿⣿⡏⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⣿⣿⣿⡿⢿⣿⣷⣠⣾⠏⢀⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠸⣄⡼⠀⣠⠞⣽⣿⣿⡇⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⣿⣿⣿⣷⣹⣿⣿⠁⠀⣼⣿⣿⣿⣄⠙⢿⣿⡈⠙⠲⠦⣽⠷⠚⠁⣸⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⣿⣧⣿⣿⣿⣿⢧⣿⡏⢰⣾⣷⣿⣿⣿⣿⣦⠀⠙⣇⠀⢠⡞⠁⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀ ⠙⣿⣷⣯⣽⣿⣿⣿⠇⣴⠟⠿⣿⣿⣿⠋⠀⠀⠀⣸⠀⠈⣳⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀ ⠀⣾⣿⣿⣬⣻⣿⢃⣼⡇⠀⠈⠛⣿⣿⠀⠀⠀⣴⣿⠀⠀⢹⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣾⣿⡷⢿⣶⡾⠿⢷⡀⠀⣼⣿⣿⠀⠀⢸⠀⢸⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⠀⢿⣿⣟⣚⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣿⣶⣿⣿⣿⡄⠀⢸⡄⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣹⣸⣿⣿⣿⣿⣿⣿⣷⡀⠀ ⠀⢸⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⣀⣀⠀⣸⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣏⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⡿⢁⣤⡤⣤⣤⣤⣤⡤⢐⣲⣂⣒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠾⣿⣷⣿⣧⣧⣴⣷⣤⠊⣨⢔⣉⡉⠻⣷⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⢸⢰⣿⡭⠯⠁⠀⠀⠈⢂⣤⡿⡿⣿⢟⠷⣫⢽⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⠰⢸⣯⣿⣶⣤⣤⣤⡌⠁⣧⣶⣤⣿⣿⠰⡱⠿⢤⣬⣉⣀⡒⠀⠤⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠗⡨⢛⢺⣾⣿⣿⣿⣷⣶⣿⣿⣿⣿⣇⡇⣷⣶⣤⣤⣄⣉⡉⠛⠛⠲⠶⢦⣬⡭⠀⢩⡾⠄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠷⣶⡤⠌⢛⣛⣿⡧⣶⠉⠉⠩⢽⣾⣿⣿⣿⣧⣄⣀⣍⡉⠛⠛⠿⠿⢶⣶⣦⣤⠃⢠⣛⣛⠛⠿⠒⣖⣼⣭⡤⣶⣒⡠⡤⡀⠀ ⠀⢀⠔⠽⢍⢑⣾⣟⣿⣷⣃⡳⣩⣾⣿⣿⣿⡿⠿⠿⠟⠈⠉⠈⠑⠊⠖⠤⢦⣍⣩⣤⣼⠿⠿⠿⡿⢷⢰⣶⣬⢱⣉⡛⣞⣿⣿⠃ ⠀⡨⣉⠃⢠⡞⠜⡍⠉⢩⠙⠉⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠓⠒⠂⠤⢯⣉⣙⡞⠻⢗⠿⣿⡽⠆ ⢠⠶⠆⣄⣽⣦⢵⣥⣤⣼⣧⣤⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠾⠻⠃⠀ ⢸⣿⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⣿⣿⣧⢉⣽⣿⣿⣿⡟⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢿⣿⣿⣾⣿⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⡿⣿⣿⣷⣿⣿⣿⣿⣾⡳⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⣿⠿⠓⢋⠩⠉⢄⠠⢀⠄⣀⢀⠉⡉⠛⠓⠯⢿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠛⡉⢄⠂⠜⣀⠣⠉⡄⢊⠔⠨⡀⠎⠰⣀⠣⢌⡐⠠⢈⠙⠾⣟⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⠟⡉⢐⡐⠰⠈⠌⢂⡐⠠⢃⠐⣈⠐⠡⠘⣀⠃⡄⠒⠠⠘⡐⠂⠌⡐⢈⠛⢿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣿⡿⠛⠠⡘⠠⠀⠇⡘⠸⢀⠠⠃⡜⢠⠀⠜⢃⠣⢀⠜⣀⠛⠄⢣⢀⠛⢠⠘⡀⠄⡀⠘⣿⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⠟⢀⠡⢂⠅⠡⠃⡌⠐⡁⢢⣀⣃⠐⢂⡉⢌⠂⣁⢊⠐⢂⣉⡌⢄⠢⠉⢄⠂⢅⠘⠠⢁⠘⢻⣳⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⣿⠋⠄⢃⠘⡀⠎⡐⠡⢀⢃⣴⣿⣿⡿⠈⠤⠐⠤⠡⠄⢢⠈⠼⣿⣿⣦⡠⢉⠐⠌⢂⠌⢡⠂⠌⠄⢿⣽⣄⠀⠀⠀⠀⠀ ⠀⠀⢀⡾⣿⠣⡉⠄⠃⠌⡐⠐⣠⣡⣶⣿⣿⡿⠋⠠⡁⢆⠩⢐⠡⢘⠠⠌⠠⠙⢿⣿⣿⣦⣌⣄⠃⠌⠠⠉⢆⡈⠄⣻⡽⡆⠀⠀⠀⠀ ⠀⠀⣾⣹⠇⠠⡑⡈⠴⣿⣿⣿⣿⣿⠿⠟⢉⠠⠌⢂⠑⡠⢊⠐⠌⢂⠑⡨⠑⡈⠄⡈⠻⢿⣿⣿⣿⣿⣶⣅⢂⡐⠐⡈⢷⣻⡀⠀⠀⠀ ⠀⢠⣿⡟⠈⡅⢒⡀⠆⠹⢛⠋⡉⠄⢂⠌⢂⢂⡉⠤⢁⠰⡀⢎⡐⢡⠈⡄⡑⢈⠤⢁⠂⡄⠠⠉⢯⣿⣯⣿⣷⣆⠡⠈⠼⣿⣇⠀⠀⠀ ⠀⢸⡷⡇⡑⠌⡄⠢⢘⠠⠉⢄⢡⠌⢂⠘⠠⠂⠔⠢⢈⡐⢀⠂⡐⠠⠁⡔⠈⡄⠢⠌⡐⠠⠡⠈⣿⢿⡟⣻⣯⣿⣦⣅⣒⣿⣿⡀⠀⠀ ⠀⢸⣟⡇⢈⠖⠠⡑⢂⠢⢁⠂⠌⣿⣦⣌⣡⠘⢠⢁⣂⣴⣾⡶⣵⣷⣬⣀⣡⢈⡐⣐⣠⣵⣾⡓⢹⣯⠿⣔⠣⢞⣼⣻⣿⣿⣯⠽⢳⣦ ⠀⢸⣿⡇⠰⠎⡰⠀⢇⠰⠁⠎⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣿⣿⡆⢿⣷⠈⢰⢿⣿⣿⣿⣿⣆⣹ ⠀⢸⣷⡇⢂⠱⢀⠃⢢⠐⠡⢊⠄⠡⢈⠻⠿⣿⣯⡿⠟⢋⠐⡈⠔⠠⠙⠻⢷⣿⣽⠾⠟⠡⣨⣾⣿⣻⣿⠠⠹⣿⣦⣿⣿⠿⣿⣿⣿⣿ ⠀⠘⣯⣷⡀⠃⡌⢨⠐⡈⢅⠢⢈⠅⢢⠐⡠⠀⡔⢠⠈⡄⢊⠔⡉⢄⠃⡌⠠⡀⠄⣂⣼⡿⣻⣿⣿⣿⣟⣧⡱⣈⣿⣿⢻⣿⣿⣿⣯⢿ ⠀⠀⢹⣞⣧⠐⠨⠄⡑⢨⠀⠆⢡⠈⠔⡨⢐⠡⠐⡠⠁⠌⡐⠠⢂⠂⠌⠠⠑⢠⣸⡟⢡⢛⣿⣿⣿⣿⣿⣾⣟⠦⣿⣿⡼⣿⣿⣿⡿⣻ ⠀⠀⠀⠻⣞⣧⠁⡘⡐⢂⡁⠊⢄⠊⡰⠐⡈⢂⣡⣶⣥⣮⣤⣵⣤⣬⣦⣵⣬⣿⠛⣷⡌⢎⠜⣿⣿⣿⡿⣛⢿⣮⠽⣿⣻⡽⣯⣽⡾⣟ ⠀⠀⠀⠀⠻⣎⢷⢀⠰⠁⠤⡉⢄⠂⡁⢆⢁⠂⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠠⠙⣿⡐⢮⢽⣿⡳⣉⠜⣬⣻⣧⣹⣳⢟⣵⣯⣟⡦ ⠀⠀⠀⠀⠀⠙⣮⡳⠂⡉⠔⡐⡈⠤⠡⢈⠤⢉⠰⠐⡠⢂⠔⡠⢂⠔⡠⢂⠔⡈⢆⠡⢹⣇⢼⣾⢿⠿⣧⣿⠿⣿⣿⣧⣿⣾⣿⣿⢯⣗ ⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣌⠐⡈⠄⠣⠄⠂⢆⠨⠐⡁⠂⡔⠐⠂⡔⠠⠂⡔⢈⠄⢢⠀⠛⠛⣯⢋⠚⡠⢀⡆⡹⣿⣿⣮⣟⣾⣹⣯⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣬⣷⣴⠈⡄⠉⠒⢨⠀⠃⡔⢡⠀⢣⢡⡄⠃⢡⠐⢨⠐⢡⠈⠂⢹⣿⣧⣧⢹⢻⢱⠓⣦⢻⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢭⣳⡦⣥⣂⠂⡉⡐⠐⡈⠌⣀⠂⠔⡈⢂⠑⢂⠰⣀⣮⣴⣿⣏⡘⡙⠛⠿⠻⢿⢻⣿⣿⣿⣿⣿⣿⣧ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢭⣟⣷⣶⡥⢶⡴⣤⢬⢦⡴⣥⣾⣶⣟⡯⠿⠛⣯⢷⠤⣩⢙⡶⣟⢦⣏⣿⣿⣿⣿⣿⢿⡽ ⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠘⣧⣶⡝⣛⢻⢛⡟⢻⣛⣿⣿⣿⣷⠋⢀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣻⣦⣋⣞⣼⣗⣞⣾⣿⣟⠁⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣿⣿⣴⣤⣴⣤⣶⣴⣦⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠒⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⠉⠁⠁⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠛⠛⠙⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⠏⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠂⠀⠀⢺⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⣤⣀⣄⣤⣠⣤⣤⡤⠤⠤⢤⣀⣤⡀⠀⠀⣰⠀⠀ ⢰⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⠿⣿⣿⣿⠿⠧⠴⠛⠛⠒⠛⠉⠉⠋⠉⠉⠉⠉⠙ ⢸⣿⣿⠿⠏⠉⠁⠀⢰⣿⠁⠀⠉⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⢿⠷⢶⣄⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⠁⠘⠶⣾⠟⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠈⢿⣿⠿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⡀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠙⣷⡀⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣦⣤⣤⣤⣤⡶⠋⠀⠀⠀⠀⠀⣸⡇⣿⣾⣉⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢶⣦⣤⡾⠟⠀⣿⢸⠋⣻⠾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣮⡟⢛⡶⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⠻⣶⡶⠟⣷⣤⣭⠛⢷⣤⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣴⣿⢻⡄⠘⣿⣿⣷⠋⣦⠽⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣼⣿⣿⡇⢻⣆⠸⣿⣿⡟⠙⣷⢾⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣾⣿⣿⣿⣿⣠⣿⣆⠹⣿⣿⣟⠙⣷⠿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠹⣿⣿⣿⠉⣻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣉⣿⠟⢿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⢿⣯⣟⡿⣾⡿⠋⠁⣿⣿⠀⢀⣿⣇⠈⠻⣿⣿⡾⣽⣻⣟⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⢯⣟⡿⣾⣽⣿⡟⠁⠀⣼⣿⣿⣿⣿⣿⣿⣆⠀⠈⣿⣿⣟⣷⣻⢾⣽⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⣽⣻⣞⣿⣳⣿⣿⡆⠀⣼⣿⡏⠙⠿⠿⠀⢻⣿⣧⠀⣼⣿⣿⢾⡽⣟⣾⡽⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢯⡿⣽⣳⡿⣾⣽⣻⣿⣷⡈⢿⣿⠁⣀⠀⢀⣄⠀⣿⣿⣸⣿⣿⣟⣯⡿⣯⡷⣟⣿⣻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣯⢿⣽⣻⣷⣿⣷⣿⡽⣿⣿⣿⣶⣷⣴⣿⣷⣶⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣻⣞⡷⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣞⣯⡷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣿⣽⣻⣿⣿⣿⣽⣻⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⣧⢿⣻⢷⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⣞⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡐⣉⠛⣿⣍⠋⡍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣧⠄⠒⣈⠣⠘⢸⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠈⠐⠀⠂⠁⠚⣿⣿⣿⣟⢻⣿⣭⠉⠁⠌⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣧⡀⢿⣿⣿⣿⡏⠀⠀⠀⠀⣺⣿⣻⣿⣿⣿⣿⣿⣿⣼⢾⣿⣿⣿⣿⣿⣿⣤⣄⣀⠀⠀⠀⠀⠀⠐⣀⠠⣀⣶⣼⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢾⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⡇⠀⢠⣴⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⢹⣿⣿⣯⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⠇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠈⠉⠁⠙⢿⣿⣯⢿⣽⣻⣟⡿⣿⢿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⢯⣟⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣿⣿⣷⣙⠿⣿⣿⣿⣿⣟⣡⣿⣿⣿⣿⠃⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠀⠀⠀⠀⠀⢘⣿⣿⣿⣾⣷⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣻⢾⡽⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⣰⣿⡟⠻⢻⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⡀⣾⣿⣿⣛⡟⣿⢻⣟⡿⣻⢟⡿⣽⣻⣿⣯⠀⠀⠀⠛⣿⣿⣿⣿⢯⣿⣳⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⠁⠀⣼⣿⠉⠀⠠⠘⠷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⡁⣹⣿⣿⣳⡝⣾⡱⢯⣞⡽⣳⢯⣛⣷⣻⣿⣿⡀⠀⠀⠀⣸⣿⣿⣿⣿⣳⣿⣟⣾⣻⢿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣤⡉⠿⣿⣿⡇⠀⣾⣿⣧⡀⠀⠀⠀⠀⠀⢿⡟⣿⣿⡟⠁⠀⠀⠀⠀⣿⣿⣿⣿⣯⢳⡽⣲⡝⣯⢞⡵⣯⢏⡿⣞⣳⢿⣿⣿⣦⣤⣶⣿⣿⣿⣿⣿⣷⣻⢿⣿⡽⣯⡿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣾⣿⡿⣹⣿⣿⣿⣷⣀⣀⣷⣼⣿⣿⣅⠀⠀⠀⠀⢸⣿⣿⢻⡵⣞⢯⡳⣇⠿⣜⡯⣽⢞⣯⣟⣭⣟⣻⣞⢿⣿⣿⣿⣿⢿⣟⣿⣿⣿⣿⣻⣞⣿⣽⣻⣽⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣽⣿⣿⣼⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣷⣿⠟⠻⠿⢿⣿⡿⠿⢛⣯⠻⣿⣦⡀⠀⢀⣿⣿⢏⡷⣽⢮⢷⡹⣎⣿⡹⣞⣧⣟⡾⣞⡵⣯⢷⣞⡿⣞⣷⣻⢾⣟⡾⣿⣿⣿⣿⣿⣻⣞⣷⢯⣷⣿⣾⣿⠿⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠨⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠡⠁⠚⣿⣿⣿⣿⣿⣟⡯⣞⢧⡟⣧⢿⣱⡗⣯⡽⡶⣯⡽⣏⡿⣽⣻⢾⣽⣻⢾⣽⣻⣞⡿⣽⣿⣿⣿⣿⣳⣿⣾⣿⠿⠋⠁⠀⠀⠀⢹⣿⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠃⣿⣿⣿⣯⣿⣟⣿⣿⣵⣿⣿⣿⡿⠋⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣟⣞⡷⣭⣟⡾⡽⣏⡾⣽⣳⣻⣽⣳⠿⣽⣻⢷⣯⣟⣾⣽⣻⣞⣷⣻⢿⣷⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠐⡀⠄⡀⢀⠈⡑⢶⡄⠀⠀⠀⢀⣠⣿⡟⣿⣿⢷⣻⢾⣽⣳⢯⣽⣻⣽⣻⣗⣯⢷⣯⣟⣿⣳⢯⣟⣾⡽⣞⣷⡿⣽⣾⣟⣿⣾⣿⣿⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣵⣮⣴⣡⣒⣠⣀⣬⣤⣴⣾⡿⠛⠛⣷⣿⣿⡿⣽⣻⡾⣽⣯⢷⣟⣾⣳⣟⡾⣟⣾⣽⡾⣽⣟⣿⢾⣟⣿⣯⣿⢿⣳⣿⣿⣿⣿⡧⠀⢻⣿⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⢸⣿⣿⣿⣹⡟⣷⣿⢻⣾⡟⣿⣾⣏⣿⣿⡟⣿⣾⣿⡟⣿⣾⣿⣿⢻⣾⣿⣿⣿⣷⣿⣿⣿⠁⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣻⣽⣿⣻⣿⣯⣿⣿⢿⣾⣿⣾⣿⣟⣿⣾⣿⣿⣟⣿⣾⣿⣿⣯⣿⣾⣿⣿⣿⡟⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄ ⠀⠀⠀⠀⠹⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⡀⢆⠰⡀⠤⣠⠄⠀⠀⠀⠀⣴⣿⣿⡿⣾⣿⣟⣿⣿⣻⣽⣿⢿⣿⣿⣯⣷⣿⣿⣿⣿⣽⣾⣿⣿⣟⣿⣾⣿⣿⣽⣾⣿⣿⡇⠀⠀⢸⣿⠀⠀⠀⣰⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⢹⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣦⣷⣼⣦⣴⣿⣶⠄⠀⢀⣿⣿⡿⣽⣳⣟⡾⣿⣽⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣾⣿⣟⣿⣿⣷⠀⠀⢸⣧⠀⠀⢸⡿⠀⠀⠛⠀⠀⠀⠀⣠⣶⡶⢾⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣍⠋⠙⠛⠛⠛⠛⠛⠙⠋⠉⠀⠀⣼⣿⣿⣿⡽⣳⡽⣺⣽⣳⢯⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⡽⣾⢿⣿⣿⡄⠀⠘⢿⣄⡀⢸⣧⠀⠀⠀⠀⠀⣀⣼⣿⣿⣧⣿⣿⣿⠿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⡟⢤⠐⢶⣶⣤⡀⠄⡀⠀⠀⠀⣼⣿⣿⣿⡿⣼⡳⢿⣳⢧⣟⣻⣞⣷⣻⣽⣾⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⡿⢿⣽⡺⢯⣷⣻⡽⣯⢿⣿⣷⠀⠀⠈⠻⢿⣿⣿⣷⣄⣀⣀⣰⣿⣿⣻⣿⣿⣿⠿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠙⢿⣿⣿⣶⣭⣾⣿⣿⣷⣠⣴⣷⣶⣿⠿⠋⣿⣿⣟⣶⣻⣏⣷⢻⣞⣷⣻⢾⣽⣻⣿⣿⣿⡇⠁⠸⣿⣿⣿⣟⢷⣻⡟⣶⡻⣟⣾⣳⢿⣽⣻⣿⣿⡀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣿⡿⠿⠿⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠻⠛⠿⠛⠛⠛⠋⠁⠀⠀⠀⣿⣿⣟⢶⣻⣼⡳⣟⣾⣳⢯⣿⡽⣿⣿⣿⣿⠃⠀⠀⢻⣿⣿⣞⣯⢷⣹⢷⡻⣽⢾⣽⣻⢾⡽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣮⢳⣞⣽⢻⡼⣯⣟⣾⣟⣿⣿⣿⣿⠀⠀⠀⠸⣿⣿⣞⣧⠿⣽⠾⣝⣷⡻⣾⡽⣯⣟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣎⡾⣜⣳⡿⣔⣫⢷⣭⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣾⣶⣧⣝⡎⣷⢚⡼⣳⣯⡳⢷⣻⣷⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠛⠛⢿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⢀⣠⣾⣿⣿⣿⡿⣋⣴⣿⣿⣿⣿⣿⣿⠟⣂⠐⣠⠈⠒⣁⠀⠹⣮⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣡⣦⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⢎⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡌⠓⢍⡻⠿⢀⠛⢛⣠⣿⣿⣿⣿⣦⣝⠿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣀⠹⢿⣿⣿⢟⣡⣾⣿⣿⣿⣿⣿⡿⢛⣵⣿⣿⣦⣤⣤⣂⢻⣶⣀⠘⢇⢻⣿⣿⣿⣿⠿⡡⢊⣴⣟⢿⣷⡅⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣰⣿⣦⡑⡝⢿⣿⣿⣿⣿⣿⡿⢣⠞⠀⢰⣦⢈⠐⠞⢰⣦⣝⠿⣿⣿⣿⣿⣿⣷⣮⡛⢿⣿⣿⣿⣶⣄⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣦⠸⣿⣶⠷⢋⣴⣿⣿⣿⣿⣿⣿⠟⣫⣶⣿⣿⣿⣿⣿⣿⡟⣛⢣⠹⣷⠄⢂⣰⣿⣿⡿⢋⠐⣴⣿⣿⣿⣯⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣾⣿⣿⣿⣷⣌⠢⡙⣿⣿⣟⣿⠱⣏⠀⣶⡿⢁⣾⣷⣾⣿⣿⣿⣷⣬⡻⢿⣿⣿⣿⣿⣿⣶⣝⠻⣿⣟⠉⣶⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⢻⣷⡙⣡⣾⣿⣿⣿⣿⣿⡿⢛⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⡴⠚⢀⠀⠲⣿⣿⡿⠋⠐⣤⣿⣿⣿⣿⣿⣿⣿⣽⢿⣿⣤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣴⣿⣿⣿⣿⣿⣿⣿⣷⣌⠢⡻⣿⣿⣷⣤⣙⠻⢰⣄⠆⣙⣿⣿⣿⣿⣿⣿⣿⣦⣝⢿⣿⣿⣿⣿⣿⣷⣬⡛⢿⡟⣼⡿⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠎⢻⣧⡙⣷⡌⢿⣿⣿⣿⠿⣋⣴⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠿⢋⣴⡼⢻⣾⡤⠘⠩⢂⣴⡻⣿⣿⣿⣿⣜⢿⣿⣿⣿⣯⣻⣿⣷⣤⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⣿⣿⣿⣿⡟⣵⣿⣿⣷⣌⠪⡙⢿⡿⠉⣰⣦⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡻⣿⣿⣿⣿⣿⣿⠇⣴⡿⣡⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣤⡛⡗⢮⡙⣆⡙⢷⡜⢿⣦⠹⡿⣡⡖⣛⢻⣿⣿⣿⣿⣇⣂⣿⠿⠋⣤⡾⡈⠹⢻⣺⣿⠂⠀⠠⠻⣿⣿⣟⢿⣿⣿⣿⣷⡝⣿⣿⣿⣿⣿⣿⣿⣿⣬⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿⣿⡿⢫⣾⣿⣿⣿⡟⣿⣷⡌⠂⣀⢻⣏⠝⣿⣷⢈⣝⠿⣿⣿⡟⠛⢿⣿⣿⣿⣿⣿⣦⡙⢿⣿⡿⢣⣾⢏⣼⠟⣡⠻⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣞⠳⢦⡙⢬⢣⡹⣐⢣⢌⢻⣦⡻⣷⡔⢿⣧⣥⣼⣿⣿⣿⣿⡿⢃⠁⠄⢂⠹⣿⠻⢢⣴⡲⠊⠀⠀⠀⠈⠬⣿⣿⣧⡝⣿⣿⣿⣿⣮⡻⣿⣿⣿⣿⣿⣿⢿⣿⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣦⣼⣿⣿⣿⣿⣿⣿⣿⡿⢋⣼⣿⣿⣿⡿⢫⣿⣿⠟⠁⠀⠁⠘⣿⣓⠛⠂⣼⢻⡗⢈⠙⢷⣶⣾⣿⣿⣿⣿⠐⠶⢹⣦⢛⣴⡿⣣⣾⠋⡔⡎⡵⢪⡜⡹⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣄⠲⡍⠶⣉⠓⢦⡙⢆⡣⢖⡩⢎⢎⡤⠙⢷⡌⠋⠀⠉⠛⠻⣿⠿⢋⠡⣔⢪⠵⢸⡀⠀⠀⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⢈⠻⣿⣿⣦⡻⣿⣿⣿⣿⣦⡻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⣿⣿⣿⡿⢫⣼⣿⣿⠋⠀⠀⠀⠀⠀⠈⠋⠿⣌⡉⠚⠁⢃⠌⣲⢈⡙⠿⣿⣿⣿⣿⡾⠟⢡⣾⢏⣴⠟⢡⣚⠱⡜⢲⠱⣌⡱⠣⢞⠳⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⣰⣷⣶⣶⣶⣶⣶⣶⣴⡖⢒⡒⣴⣶⣶⣶⣶⣾⣶⣤⠄⠀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀ ⠀⠉⠉⠉⠉⠉⠉⠻⣿⠛⠛⢻⠛⢿⣿⣿⣿⣿⣿⡟⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣌⣀⠸⢿⣿⣿⣿⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⠉⠉⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠉⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠛⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣦⣤⣤⣄⡀⠀⢀⣠⣾⣿⠿⠋⠀⠀⠀⠀⠀⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠞⣿⠟⠋⠉⠉⠙⣻⠿⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⡼⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⢠⡞⠁⠀⠀⠀⢀⡴⠋⠀⢀⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢠⠏⠀⠀⠀⠀⣰⠏⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡥⠤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⠀⣠⡏⠀⠀⠀⠀⣼⠁⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣄⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⠋⠀⠀⠀⠀⢸⣧⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣾⡿⠿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳ ⠀⠀⠀⠀⠀⠀⢀⣾⠿⠛⢿⣿⣷⣄⡀⣿⠃⠀⠈⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣤⣦⣼⣿⠀⠀⠀⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⡿⠋⠉⠉⠁⠀⠀⠀⠀⠉⢯⡙⠻⣿⣿⣷⣤⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠃⢀⡤⠖⠋⠉⠉⠉⠉⠉⠉⠒⠦⣄⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠄ ⣾⣿⠋⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠙⢦⣄⠉⠻⢿⣿⣷⣦⡀⠀⠈⠙⠛⠛⠋⠀⢰⠟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⠀⠀⠀ ⣿⡇⠀⠀⠀⣴⠟⣫⣿⣿⣄⠀⠀⠀⠀⡶⢌⡙⠶⣤⡈⠛⠿⣿⣷⣦⣀⠀⠀⠀⠀⡇⠀⢻⣄⠀⠀⣠⢷⠀⠀⠀⠀⠀⡶⠀⠘⡆⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⢸⣟⢸⣿⣿⣿⣿⠀⠀⠀⠀⡇⠀⠈⠛⠦⣝⡳⢤⣈⠛⠻⣿⣷⣦⣀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠛⠦⠤⠤⠚⠁⠀⠀⢳⠀⠀⠀⠈⠛⠿⠿⠿⠟⠋⠀⠁⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠈⢿⣞⣿⣿⣿⠏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⠳⢬⣛⠦⠀⠙⢻⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⣿⠉⢻⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⣠⣄⠀⠀⢰⠶⠒⠒⢧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⡟⢿⣷⣦⣴⣶⣶⣶⣶⣤⣔⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⣤⠀⠀⠿⠿⠁⢀⡿⠀⠀⠀⡄⠈⠙⡷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⡇⠀⣿⠙⣿⣿⣉⢉⠙⠿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠙⠷⢤⣀⣠⠴⠛⠁⠀⠀⠀⠇⠀⠀⡇⢸⡏⢹⡷⢦⣄⡀⠀⠀⠀⣿⡀⢸⡇⢸⡇⠀⡟⠀⢸⠀⢻⡷⢦⣄⣘⣿⡆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠢⣤⡀⠀⠀⠀⠀⠀⠀⣠⠾⣿⣿⡷⣤⣀⡇⠸⡇⢸⡇⢸⠉⠙⠳⢦⣄⡻⢿⣾⣧⣸⣧⠀⡇⠀⢸⠀⢺⡇⢤⣈⠙⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⣿⣷⣌⡉⠛⠲⢶⣶⠖⠛⠛⢶⣄⡉⠛⠿⣽⣿⣶⣧⣸⡇⢸⠀⠀⠀⠀⠈⠙⠲⢮⣝⠻⣿⣷⣷⣄⣸⠀⢸⡇⠀⠈⠁⠀⢸⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠻⢿⣷⣶⣤⣉⡻⢶⣄⣀⠈⠙⠳⢦⣈⡉⠻⢿⣿⣷⣾⣦⡀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢭⣛⠿⣿⣷⣼⡇⠀⠀⠀⠀⠈⣿⡇⠀⡈⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣶⣽⣻⡦⠀⠀⠈⠙⠷⣦⣌⡙⠻⢿⣟⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢯⣻⡇⠀⠀⠀⠀⠀⢸⣿⠀⣀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢀⡏⠙⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣶⣤⣤⣤⣀⣈⠛⠷⣤⣈⡛⠷⢽⡻⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⢤⣀⠀⠀⢸⣿⡀⠈⠳⢤⣀⣀⣰⠃⠈⠛⠶⠶⠿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⠛⠉⠙⠛⠛⠻⢷⣦⣄⣩⣿⠶⠖⠛⠛⠛⠛⠛⠛⠿⢷⣶⣦⣄⠀⠀⠀⠀⠉⢻⣶⣿⣿⠇⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠀⠀⠀⠀⠀⣠⠖⠂⠀⠀⠀⠈⠙⠿⣿⣦⡄⠀⠀⣸⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣰⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣄⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠙⢿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠦⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠄⠙⡿⠿⠦⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⠉⠉⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠉⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠛⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣦⣤⣤⣄⡀⠀⢀⣠⣾⣿⠿⠋⠀⠀⠀⠀⠀⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠞⣿⠟⠋⠉⠉⠙⣻⠿⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⡼⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⢠⡞⠁⠀⠀⠀⢀⡴⠋⠀⢀⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢠⠏⠀⠀⠀⠀⣰⠏⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡥⠤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⠀⣠⡏⠀⠀⠀⠀⣼⠁⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣄⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⠋⠀⠀⠀⠀⢸⣧⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣾⡿⠿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳ ⠀⠀⠀⠀⠀⠀⢀⣾⠿⠛⢿⣿⣷⣄⡀⣿⠃⠀⠈⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣤⣦⣼⣿⠀⠀⠀⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⡿⠋⠉⠉⠁⠀⠀⠀⠀⠉⢯⡙⠻⣿⣿⣷⣤⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠃⢀⡤⠖⠋⠉⠉⠉⠉⠉⠉⠒⠦⣄⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⠋⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠙⢦⣄⠉⠻⢿⣿⣷⣦⡀⠀⠈⠙⠛⠛⠋⠀⢰⠟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⣴⠟⣫⣿⣿⣄⠀⠀⠀⠀⡶⢌⡙⠶⣤⡈⠛⠿⣿⣷⣦⣀⠀⠀⠀⠀⡇⠀⢻⣄⠀⠀⣠⢷⠀⠀⠀⠀⠀⡶⠀⠘⡆⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⢸⣟⢸⣿⣿⣿⣿⠀⠀⠀⠀⡇⠀⠈⠛⠦⣝⡳⢤⣈⠛⠻⣿⣷⣦⣀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠛⠦⠤⠤⠚⠁⠀⠀⢳⠀⠀⠀⠈⠛⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠈⢿⣞⣿⣿⣿⠏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⠳⢬⣛⡦⠄⠙⢻⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣻⣽⠫⣿⠉⢻⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⣠⣄⠀⠀⢰⠶⠒⠒⢧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠡⣿⠀⢸⡇⢸⡟⢿⣷⣦⣴⣶⣶⣶⣶⣤⣔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⣤⠀⠀⠿⠿⠁⢀⡿⠀⠀⠀⡄⠈⠙⡷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⡇⠀⣿⠙⣿⣿⣉⠉⠙⠿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠙⠷⢤⣀⣠⠴⠛⠁⠀⠀⠀⠇⠀⠀⡇⢸⡏⢹⡷⢦⣄⡀⠀⠀⠀⣿⡀⢸⡇⢸⡇⠀⡟⠀⢸⠀⢹⡷⢦⣄⣘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠢⣤⡀⠀⠀⠀⠀⠀⠀⣠⠾⣿⣿⡷⣤⣀⡇⠸⡇⢸⡇⢸⠉⠙⠳⢦⣄⡻⢿⣾⣧⣸⣧⠀⡇⠀⢸⠀⢸⡇⢤⣈⠙⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⣿⣷⣌⡉⠛⠲⢶⣶⠖⠛⠛⢶⣄⡉⠛⠿⣽⣿⣶⣧⣸⡇⢸⠀⠀⠀⠀⠈⠙⠲⢮⣝⠻⣿⣷⣷⣄⣸⠀⢸⡇⠀⠈⠁⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠻⢿⣷⣶⣤⣉⡻⢶⣄⣀⠈⠙⠳⢦⣈⡉⠻⢿⣿⣷⣾⣦⡀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢭⣛⠿⣿⣷⣼⡇⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣶⣽⣻⡦⠀⠀⠈⠙⠷⣦⣌⡙⠻⢿⣟⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢯⣻⡇⠀⠀⠀⠀⠀⢸⣿⠀⣀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢀⡏⠙⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣶⣤⣤⣤⣀⣈⠛⠷⣤⣈⡛⠷⢽⡻⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⢤⣀⠀⠀⢸⣿⡀⠈⠳⢤⣀⣀⣰⠃⠈⠛⠶⠶⠿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⠛⠉⠙⠛⠛⠻⢷⣦⣄⣩⣿⠶⠖⠛⠛⠛⠛⠛⠛⠿⢷⣶⣦⣄⠀⠀⠀⠀⠉⢻⣶⣿⣿⠇⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠀⠀⠀⠀⠀⣠⠖⠂⠀⠀⠀⠈⠙⠿⣿⣦⡄⠀⠀⣸⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣰⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣄⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠙⢿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠦⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠄⠙⡿⠿⠦⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠒⠦⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⣤⡄⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⢡⠉⠉⠉⠉⠉⠑⠒⠒⡶⡄⠀⠀⠀⢸⠁⠀⠘⠃⠀⠀⢀⠀⠀⠇⠀⠀⠀ ⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠯⠽⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⡏⠀⠒⠦⣄ ⡖⠒⢺⠀⠀⣴⢲⡖⠒⠒⠒⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⡃⠀⠈⠀⠀⢀⡇ ⡇⠀⢸⠀⠀⣏⠛⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢹⠒⠚⠛⠋⠉ ⠓⠒⢸⠀⠀⣇⠀⠀⠉⠲⢄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠸⠤⣤⠇⠀⠀⠀⠀⠀⠉⠲⠤⣄⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⣩⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠓⠒⠒⠒⠚⠁⡇⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢳⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠰⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠇⠀
⢀⡴⠑⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡇⠀⠿⡀⠀⠀⠀⣀⡴⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⢄⣠⠾⠁⣀⣄⡈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⠁⠀⠀⠈⠙⠛⠂⠈⣿⣿⣿⣿⣿⠿⡿⢿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⣁⣀⠀⠴⠂⠙⣗⡀⠀⢻⣿⣿⠭⢤⣴⣦⣤⣹⠀⠀⠀⢀⢴⣶⣆ ⠀⠀⢀⣾⣿⣿⣿⣷⣮⣽⣾⣿⣥⣴⣿⣿⡿⢂⠔⢚⡿⢿⣿⣦⣴⣾⠁⠸⣼⡿ ⠀⢀⡞⠁⠙⠻⠿⠟⠉⠀⠛⢹⣿⣿⣿⣿⣿⣌⢤⣼⣿⣾⣿⡟⠉⠀⠀⠀⠀⠀ ⠀⣾⣷⣶⠇⠀⠀⣤⣄⣀⡀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠉⠈⠉⠀⠀⢦⡈⢻⣿⣿⣿⣶⣶⣶⣶⣤⣽⡹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠲⣽⡻⢿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣮⣭⣽⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠛⠉

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⠀⠀⠀⠀⠶⠀⢠⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡀⠀⠀⢀⣤⡀⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠟⠀⠀⠹⠿⠇⢰⠄⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠉⠀⠠⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠲⡆⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠈⣀⡀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿ 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⠀⠀⠀⠀⣤⣦⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⢀⣴⣶⣾⣿⣶⣶⣶⣾⣷⣶⣤⣴⣾⡇⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⡄⠀⠀⣄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⣻⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⣠⣾⣿⡿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⣠⣾⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⣿⡿⠋⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⣠⣾⣿⡿⠋⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢴⣿⡋⣠⡄⠀⠀⢸⣿⡿⠋⣠⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣡⣴⠶⢾⣿⣿⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⡟⠀⠀⠀⢹⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⣿⣤⣀⣠⡾⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠟⠉⠉⠙⢿⣿⡋⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣶⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⠙⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⢿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣶⣿⣶⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠶⠂⠒⠀⠀⠐⠂⠂⠲⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣭⣭⠛⢿⡏⠀⠀⠀⣠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣟⠉⠁⠀⠉⠁⢠⡞⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀ ⠀⠀⠀⣠⣴⣿⣿⣛⠻⠃⠀⠀⣠⣾⠋⠀⡄⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⣿⣿⣿⣿⣿⣷⣄⠀⢼⡿⠁⢀⣰⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣷⣮⡙⣿⢿⣷⠏⠀⠀⣿⣿⣺⣿⡉⠳⢄⡀⠀⠀⡴⠋⠁⠀⠀⠙⢦⡀⡴⠋⠁⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀ ⢸⣿⡟⣿⣿⣿⣿⣿⢹⣾⣿⠀⣠⣾⣇⣿⣿⣿⣿⣦⠀⠙⣆⣸⠁⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀ ⢸⡿⣷⣿⣿⣿⣿⡿⣾⣻⣏⡰⣻⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⢹⠀⢰⣿⣿⡇⠀⠀⣼⠀⠀⢰⣿⣿⡆⠀⣸⠀⠀⠀⠀⠀ ⠀⠹⡎⠻⢾⣭⡴⠞⣿⡿⠃⣠⡟⠛⠻⢿⣿⣿⡇⠀⠀⠀⠀⠈⢧⡀⠉⠋⠁⠀⡰⠛⣆⠀⠈⠙⠋⠁⢠⠇⠀⠀⠀⠀⠀ ⠀⠀⣿⣠⣤⣶⢦⣰⣿⠁⣰⣿⠁⠀⠉⠲⣿⣿⠃⠀⠤⢤⡞⠀⠀⠙⠒⠒⠒⠋⠀⠀⠈⠣⢄⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⢻⡇⣰⣿⢹⣤⣤⡀⣰⣿⣿⡁⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⡻⠿⣻⣿⣷⣿⣧⡿⠉⠉⠉⠉⠁⠀⢹⣦⣀⣧⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀ ⠀⠀⢻⣿⣯⣽⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⣸⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⣀⡴⢻⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠉⠉⠁⠀⡎⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄ ⠀⠀⠀⠻⣿⣿⣿⣿⣿⢇⠀⠀⠀⠀⠀⠀⢀⡼⠁⠈⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀ ⠀⠀⠀⠀⠘⣿⣿⡟⠛⠾⠶⠶⠶⠖⠒⠊⣹⠃⠀⠀⠀⠈⠛⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⣧⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣴⣞⡛⠋⠉⠉⠉⠙⠛⠓⠶⣤⣀⠀⠀⠀⣼⠃⠼⣧⣀⣠⣤⣤⣤⣤⣄⣀⣠⡟⠀⢹⡇⠀⣤⣶⠛⠛⠉⠉⠉⠉⠉⠉⠙⠛⠲⢦⣄⡀⠀⠀⠀⠀⠀ ⠉⠉⠉⠙⠳⣄⠀⠀⠀⠀⠀⠀⢈⣽⠗⠀⢀⣿⡀⠷⠛⠉⠁⠀⠀⠀⠀⠈⠿⠋⠀⠀⣸⠇⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣼⠁⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⢷⡀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣬⣻⣦⠀ ⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⣿⠀⣰⢟⠂⠀⠀⠀⠀⠒⡾⠳⡀⠀⢀⡴⢦⣀⠀⠀⠀⠈⢻⡄⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⠙⠃ ⠀⠀⠀⡴⠿⠖⠒⠶⣦⡀⠀⠀⠹⣧⡏⠀⠀⠀⠀⡰⠋⠁⢀⠏⠀⠀⣇⣀⣀⡇⠀⠀⠀⠀⠀⢿⣼⠃⠁⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⣭⡉⠉⠁⠀⣀⡀⠀⠀⠀⠀⠀⢠⣤⠾⠋⠁⠀⠀⠀⣠⡶⠒⠓⠶⢦⣄⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣤⠴⠶⣾⠀⠀⠀⠀⠀⢀⢻⠁⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠿⠳⢶⣦⣤⣀⠀⣿⠀⠀⠀⠀⠀⠈⠙⠷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⡄⠛⠁⠀⠀⢹⡗⠀⠀⠀⠀⠛⠉⠉⠉⠙⠛⠶⣦⠄⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠉⠳⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡖⠚⢉⠉⢁⣀⡇⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⡴⠿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣟⢻⡟⠛⠛⠛⠹⣶⢱⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⠃⠀⠀⠀⠀⠹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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