Agent 47 Emojis & Text

Copy & Paste Agent 47 Emojis & Symbols

⠱⢌⠒⡰⠐⡄⢂⠐⡀⠂⠄⠠⠀⡀⢀⡠⠀⠐⠀⠀⠀⠒⠀⢄⡀⠠⠀⠄⡀⢂⠐⡀⠆⢂⠒⡐⢆⠱⡌ ⠣⠌⢢⠑⢂⡐⢂⠐⠠⠁⠐⠀⢠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⡀⠀⠐⠀⢂⠐⡈⢂⠱⢈⠆⡱⢈ ⡁⠎⠠⡈⠄⡐⠀⠈⡀⠀⠀⣠⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣄⠀⠈⠀⠐⢀⠂⠰⠈⠤⠑⡌ ⠐⡈⠐⡀⢂⠀⠈⠀⠀⠀⠀⣯⠔⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡠⢽⡀⠀⠀⠈⠀⠈⠄⢁⠂⢡⠂ ⠡⠀⠁⠄⠀⠀⠀⠀⠀⠀⢰⣏⠞⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣓⢯⡇⠀⠀⠀⠀⠐⠈⠀⠌⡀⠂ ⠀⠂⠐⠀⠀⠀⠀⠀⠀⢀⠸⣻⢲⠴⣦⣤⣀⠀⠀⠀⠀⠀⣀⣠⣴⠦⡝⣮⡇⡀⠀⠀⠀⠀⠀⠐⠀⡁⠂ ⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣾⡿⠿⣷⢿⣿⣿⣷⡷⠑⢶⣾⣿⣿⡿⣾⠿⣵⣷⠇⠀⠀⠀⠀⠀⠀⠐⠀⡁ ⠀⡀⠀⠁⠀⠀⠀⠀⠀⠘⣿⣄⠀⠈⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠁⠀⣨⣿⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣀⣀⣠⡴⣎⣁⣀⣐⣩⠦⣄⣀⣠⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣻⢻⢯⣀⣘⣛⣻⣛⣋⣠⣽⡟⡟⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣣⡀⡙⠙⠚⠙⠓⠫⢋⠐⣼⣽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⡀⠀⠀⠀⠀⠠⢁⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠛⣿⣿⣤⣤⣤⣤⣴⣿⣿⠛⣹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠄⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣇⠀⠀⠙⢿⣿⣿⣿⠿⠋⠀⠀⣾⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠄ ⠀⡀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣨⣿⣅⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⡀ ⣠⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢀⣴⣿⣿⣿⣆⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣥ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⠞⠻⣿⣿⣿⠟⠳⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣧⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⣿⣿⣿⡄⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⣿⢿⣟⡿⣟⡿⣟⡿⣿⣻⡿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⣽⣾⣻⡽⣟⠞⠙⠉⠉⠉⠋⠳⣿⡽⣷⣻⣾⣟⣿⣿ ⣿⡿⣽⣟⣾⣽⠛⠁⢀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣷⣟⣾⣟⣿ ⣿⣷⣻⣽⢯⣟⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⣽⣯⢿⣽⣻⣿ ⣿⡾⣽⣾⡻⣽⢠⣾⣷⣤⣀⠀⣀⣤⣶⣗⣂⣸⢯⡿⣾⣽⣾ ⣿⡽⣷⢯⣟⣦⠝⠿⠿⠿⠟⠉⠻⠿⠿⠟⢏⣶⣻⣟⣷⣻⢾ ⣿⣽⢯⡿⣾⢯⣄⣀⣀⢴⣀⣀⣀⣦⣀⣀⣠⣋⣿⢾⣳⣿⣻ ⣿⡾⣿⡽⣯⣿⣝⣏⠫⢤⡝⠋⢭⡤⠟⣹⣳⡿⣽⣻⣽⣞⣿ ⣿⣟⣷⢿⣳⣯⢿⣞⣆⠀⠈⠉⠁⠀⣰⣿⣯⢿⣽⣳⡿⣾⢿ ⣿⣿⣽⡾⣿⣽⣾⢽⣿⣦⣀⣀⣀⣤⣿⡏⣿⣾⢯⣿⣳⣿⣾ ⣿⣿⣯⣿⣿⣿⡏⠀⠉⠻⣿⣿⡿⡟⠉⠀⢸⣿⣿⣿⣿⣷⣿ ⣿⣿⣿⣿⣿⣿⡀⠀⠀⢠⣿⣿⣷⡄⠀⠀⢈⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠈⠈⠉⠁⠐⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣸⢣⠎⡁⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⢢⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⣸⣥⣳⠶⠿⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠿⠲⢦⣤⡘⣰⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣿⡞⢿⣷⣶⣦⣿⣿⣿⣷⣴⡀⢀⠀⣀⢀⣤⣾⣿⣿⣿⣶⣶⣲⣾⠇⢻⡷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣻⠀⠈⠘⠛⢧⡙⠟⠻⣿⡿⠿⠃⠀⠘⠿⢿⣿⡟⠛⠟⢱⠛⠋⠁⠀⢨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⡇⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠉⠁⠀⠀⠀⢠⠶⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠀⠀⠀⠀⠀⠀⢀⡤⠖⠀⠀⠀⠀⡀⠰⠤⡀⠀⠀⠀⠀⠀⠀⢨⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣄⣀⢀⣠⡴⠋⠸⣤⣄⡄⠀⣠⣧⣤⠃⠙⠲⣄⠀⣀⣤⡾⣹⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡟⣏⢛⢣⣀⣀⠀⠙⠻⣿⣿⡟⠋⠁⢀⣀⣀⠌⡻⢩⢻⣳⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣽⣄⠀⠈⠛⠿⢹⢹⠒⠲⠐⡏⡯⠟⠛⠁⠀⣠⢯⣻⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣦⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠄⣱⣣⡟⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠼⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⡟⢡⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣷⢹⡸⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠶⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣇⢳⣩⢛⣿⣷⣤⣀⣀⣀⣀⣀⣤⣾⠟⠋⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀ ⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠪⡗⢦⢫⡔⣛⢿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⠉⠒⠹⠜⢦⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣠⣾⣿⣿⢿⡿⣿⣷⣄⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢀⠔⠁⠹⣿⣿⣿⣿⣿⠃⠈⠣⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠁⠀⠀⠀⢙⣿⣿⣿⡇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠀⠐⠂⠠⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⡇⠀⣐⠛⠛⣻⣷⣦⣄⢀⠀⣀⠀⢀⣠⣴⣾⣿⡛⠙⣢⠀⢸⡤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡇⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠒⢿⣿⣿⣿⣿⣿⣿⣿⡿⢇⣸⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⣇⠀⠀⠈⠉⠒⠒⠉⠉⠉⠀⠀⠀⠉⠉⠉⠓⠒⠉⠁⠀⠀⣹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⠀⠀⠀⠀⠀⣀⣴⠲⠄⠀⢠⡖⣦⣀⠀⠀⠀⠀⢀⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣦⣄⣤⡾⠋⢹⣶⣶⣤⣾⣶⡆⠙⢷⣤⣤⣴⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⡝⠿⣧⣤⣤⣭⣽⣿⣯⣭⣤⣤⣼⢿⢯⣟⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣵⡄⠈⠛⠛⠧⠛⠛⠙⠘⠟⠛⡡⢂⣞⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣿⡄⠱⠀⠀⠀⠀⠀⠀⢀⠜⢡⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠇⠈⠻⣿⣿⣷⣤⣀⣀⣠⣤⣾⣿⣿⠟⠁⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⡀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⢰⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠙⢻⣿⡟⠋⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⣴⣿⣿⣿⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣠⣾⣿⣯⢀⣿⣿⣷⣄⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡴⠋⠉⢿⣿⣿⣿⡟⠉⠻⢆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢈⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣼⣿⢹⣿⣇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⣿⣿⣿⣿⣿⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣸⣿⣿⣿⣿⣿⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠱⡐⢂⠐⠠⠀⠀⢄⠄⠂⠀⠀⠀⠐⠠⠀⡀⠐⡀⠂⠆⠱⣈ ⠡⠐⠠⠈⠀⠀⢠⠩⠀⠀⠀⠀⠀⠀⠀⠜⡀⠀⠀⠁⠌⡐⠄ ⠠⠁⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⢘⣧⠀⠀⠀⠀⠐⠈ ⠀⠀⠀⠀⠀⢀⣸⣕⣲⣤⣄⣀⣠⣤⣖⣺⣝⡀⠀⠀⠀⠀⠄ ⠀⠀⠀⠀⠀⠨⢧⠉⠋⠙⠉⠀⠙⠉⠙⠉⣼⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣷⢶⣋⣳⣶⣞⣱⢶⣾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣷⡈⠉⠀⠉⢁⣶⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣬⠻⢷⣦⣤⣴⡿⠟⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⣤⣶⣾⣿⣿⡄⠀⢙⣿⡋⠀⢰⣿⣿⣷⣶⣤⣀⣀⠀ ⣶⣿⣿⣿⣿⣿⣿⣿⣇⢠⣾⣿⣷⡀⣸⣿⣿⣿⣿⣿⣿⣿⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⡅⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣼⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿

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