⠀⠀⣰⠟⠉⣩⣿⣿⣿⣿⡿⠉⠉⣿⡟⠉⠉⣿⠀⢀⡴⠋⢉⠝⣀⣀⡀⠀ ⢀⡾⠁⢀⣾⣿⣿⣿⣿⠏⠀⢀⠀⠋⢀⠀⠀⣿⢰⠋⠀⠰⠥⠤⠇⠀⢸⠀ ⣏⣀⣠⣿⣿⣿⣿⣿⣟⣀⣀⣿⣀⣠⣿⣀⣸⡇⠓⠒⠒⠒⠒⢲⣀⣸⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣋⣀⣀⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⡤⠤⠤⢤⡤ ⣿⣿⣿⠿⠟⠉⠉⠀⣹⣿⣋⣻⣿⡇⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠀⠀⠀⠀⠀ ⠈⠉⠀⠀⠀⠀⠀⣴⡿⠁⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠶⠶⠶⠶⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣾⣿⣿⣤⣤⣤⣤⣤⣤⣤⣼⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⠜⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠉⠿⠏⠉⠉⠉⠉⠉⠙⠛⠛⠃ ⢸⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⣿⣿⣿⠟⠉⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠛⠉⠉⠙⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠃⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣶⣶⣶⣶⣦⣤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⣇⠈⠉⠉⠉⠉⠋⠙⠉⠁⢜⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⡿⣿⡈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣳⣿⣳⢟⣳⢯⡾⣿⢳⡯⣟⣿⣎⢻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣯⣴⡟⣷⣿⣿⣿⣾⡷⣯⢷⣟⣾⣿⣿⣄⠙⠻⠭⠭⢽⠿⠶⢶⢶⣶⡛⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⡶⠶⣶⣖⣶⣶⣶⣶⣴⣶⣶⣶⣾⣿⡟⣶⣤⣠⣄⡀⠠⣴⣿⣿⣤⣤⡙⢶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⡷⣟⡿⣿⣿⣿⡿⣿⡽⣿⣾⣿⣿⣿⣿⣶⡶⣤⣤⣤⣤⣉⣉⣉⠙⠓⣦⢙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠙⣧⠘⠳⠟⠓⠖⠀⠀⠀⠛⠛⠳⣤⠤⠤⠜⠿⠶⢾⣭⣻⠻⢿⡛⣮⣿⣿⡟⣿⣺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣾⠟⠉⠛⢻⠉⠿⠷⢶⣄⣀⡀⠀⠀⠀⢀⢸⣯⣿⡿⣽⣻⡮⣍⣭⣾⢿⡽⣿⣿⣿⣿⢿⣿⣿⣗⣯⢿⣉⣩⣭⣭⣿⣿⣿⣿⣿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣻⣤⣿⣮⣹⣿⣷⣶⣶⣶⣦⡶⢲⣾⣿⡯⠹⠿⠄⣼⣿⣧⡇⠒⣀⣽⣟⣛⢿⣿⣿⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣾⣟⣿⣿⣶⣶⣶⣶⣿⣿⣶⡶⠞⠛⣧⣴⢦⡶⠲⣴⣿⣿⣿⡱⣧⢟⣽⡳⢯⣟⡾⣿⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣨⡿⣷⣶⢶⣶⣶⣶⣶⣶⣶⢿⣿⡮⠀⢀⣨⣿⣿⢿⠿⣿⣿⣿⣿⣿⠿⣯⣿⣶⣴⣴⣶⣾⣿⣿⣷⣾⣿⡟⣿⣿⣞⣿⣿⣿⣽⠀⠀⢠⣴⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣯⣛⣷⣶⣶⣶⣟⣉⣹⠶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⣫⣉⣳⣶⡾⣿⣿⣧⣽⣿⣿⣿⣿⣿⣭⣭⣤⣯⣥⣍⣭⣿⣷⣛⣾⣿⣞⣽⣻⣞⣽⣳⣯⣿⣿⣿⣻⣿⣿⣟⣿⣿⡏⢛⣯⣿⣯⣭⡻⣿⣈⣁⣉⣯⣈⣫⣩⣟⣍⣉⣉⣙⣀⣉⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡷⠞⢻⣋⣿⣿⣿⠆⣿⢹⣿⣷⣶⣿⢉⣙⣉⣉⣏⣉⣛⣉⣿⣏⣙⢋⣹⣷⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⢿⣟⠻⣿⣻⠿⡿⢿⢿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣿⣿⣿⣻⣿⢿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣸⣿⣧⣸⣰⣿⣿⣿⣿⣀⣿⣸⢿⡟⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣾⡟⡟⠛⣿⣿⣿⣿⣿⣿⡿⣿⣿⣶⣶⣶⣷⣾⣶⣷⣾⡶⣶⣶⡾⡶⣶⢷⣾⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣷⡇⢾⣧⠀⠀ ⢸⡟⣿⣿⠋⠀⠉⠉⠀⠁⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣽⠟⠛⠛⣏⣙⣏⢙⣸⣸⣿⣿⣿⣟⣉⣋⣙⣛⣛⣛⣛⠛⠟⠛⠛⢹⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⣦⣤⣴⣦⣿⣁⠾⠇⣠⣰⣀⣤⣀⢀⣦⣀⣠⣆⠀⢠⣄⠈⣹⡍⠉⢹⡉⠉⣽⡉⠙⣿⠛⠛⣿⠛⠛⡟⠛⠛⣿⣿⣿⣿⣿⡟⣿⣛⢛⣛⢛⣛⡛⢛⡛⣟⣛⠛⣛⠛⣛⣛⣻⣛⣟⣛⠛⠛⢛⣿⣿⣟⡛⣿⢿⣿⣿⣷⣿⣷⣾⡿⠟⠿⠏⠛⣿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠟⠻⠻⠟⠿⠿⠟⠿⠿⠿⠿⠿⠻⠿⢟⡟⡿⣿⢿⢿⡿⣿⢾⣦⠀ ⢸⣷⣿⣿⣶⣶⣶⣶⣾⣶⣶⣷⣿⣾⣷⣷⣿⣿⣿⣿⣾⣿⣿⣿⣶⣾⣷⣶⣶⣾⣶⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⣿⣿⣿⣿⣯⣛⣿⣭⣭⣭⣭⣽⣿⣿⣿⣿⣶⣶⣿⣶⣾⣿⣿⣿⣿⣿⣿⠛⠛⠛⠻⠻⢿⣏⣉⢉⣿⠿⠻⠿⠛⠛⢹⢿⣷⣶⣶⣾⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣾⣿⣿⣾⣿⣷⣾⣿⣶⣶⣿⣶⣶⣿⣷⣷⣿⣿⣿⣷⣿⣷⣾⣿⣾⣿⣿⣿⣷⣾⣷⣾⣿⣶⣿⣶⣿⣿⣿⣿⣿⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣷⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣿⣶⣿⣶⣷⣿⣾⣷⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣶⢿⣧ ⢸⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠿⣿⢻⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢉⠿⣛⠟⠻⡛⢟⢻⣿⣛⣀⣀⣀⣀⣀⣰⣿⣿⣿⣿⣃⢀⣀⣀⣀⡘⢋⣹⠿⢿⣿⡿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣻⣟⣻⣻⣛⡛⣿⣿⡿⣿⢿⣿⣿⢿⣿⣿⣿⡿⣿⢿⡿⣿⢿⡿⣿⢿⡿⣿⢿⡿⣿⢿⡿⣿⢿⡿⣿⣟⡿⣿⢿⡿⢿⡿⣿⢿⡿⣿⣿⣰⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣷⣿⣾⣷⣿⣾⣷⣿⣾⣾⣶⣿⣶⣷⣾⣶⣷⣾⣶⣷⣾⣷⣿⢿⢏⣉⡙⠻⢿⢼⣿⣿⣿⡿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠷⡿⢾⡽⣿⣏⣤⡿⣙⢻⢿⣿⠙⢿⡟⡙⣿⣏⠋⣿⡟⣹⣿⣉⠻⣿⢋⠾⣿⡙⢹⣿⡩⢹⣯⠣⣿⢣⡙⣻⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣯⣿⣧⣿⣿⣽⣿⣽⣿⣧⣿⣯⣿⣿⣽⣿⣽⣿⣿⣟⣻⣉⣏⣿⣿⣭⣍⠹⣯⣽⣇⣍⣪⣔⣉⣊⣿⣜⡰⡙⣌⠧⣙⡌⣇⡛⣬⢓⡹⣌⢧⣙⣎⡳⣹⣘⣣⢛⡴⣩⣚⣥⢫⣜⣣⣽⣘⣧⣽⣹⢹⣿⠃ ⢸⣿⣿⡿⡿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⢿⠿⠿⠿⢸⣿⣿⣿⣞⡷⢺⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⡾⣷⣾⣾⣷⣷⣾⣼⣷⣯⣯⣭⣭⣽⠿⣇⣹⢯⣽⣯⣝⢻⣿⠾⣶⠿⣿⡮⢿⣾⠷⣷⣾⣿⣾⣶⡯⣶⣿⡿⣦⣶⣧⣮⣶⣿⣾⣾⣷⣷⣿⣷⣶⣿⣶⣶⡏⢯⡽⡿⢶⣮⣍⣯⣭⣉⡿⡿⢿⣿⣾⣿⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣏⠛⢷⣤⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣿⣽⣭⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣽⣿⣏⣿⣿⠏⠀ ⢸⡇⣿⣿⣦⣬⣭⣭⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠿⢿⠿⠿⠿⠿⠟⡟⠟⣯⣖⣚⡛⢻⡿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡷⣶⣄⣀⣿⡶⠶⠶⣿⣿⣶⣶⣳⣶⣿⣷⣟⣶⣞⣳⣿⣷⣶⣻⣿⣟⣾⣟⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣺⣯⣷⡾⣦⣭⣉⣿⣿⣷⣿⣞⣟⣿⣍⣩⣽⣥⣼⣿⣿⣿⠿⣿⣿⢿⡿⠻⣯⣍⣩⣉⣉⡉⢻⢿⡄⠀⠀⠈⠉⠉⠉⠙⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀ ⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠾⣷⢾⢷⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲⡿⠛⠛⠃⠁⠀⠀⠉⠁⠀⠀⠀⠁⠈⠉⠉⠙⠋⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠛⠿⣾⣥⣿⣵⣎⣩⣿⢧⣾⣿⠿⠛⠛⠁⠁⠀⠀⠀⠙⠹⣻⣿⠇⠛⠠⣟⣛⣹⣿⣟⣿⣷⣾⣿⣿⣷⣶⣾⣿⣿⣿⣯⣽⣥⣭⢹⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡻⣿⣿⣿⠛⠛⡿⣁⣼⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⠟⢻⣿⠟⢻⣿⣿⣟⡚⢿⣯⣭⡿⣻⣿⣿⣿⣻⣿⣾⣷⣿⣯⣿⣿⣿⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣸⣿⣿⣿⣿⣿⢹⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣶⠖⣴⠿⠻⠟⣻⣿⠉⠉⠉⠉⠉⠉⠉⠙⡟⢿⣿⣿⣻⡾⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⠟⣉⣿⣿⣿⣿⣿⣟⣸⣿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⣿⣿⣤⣿⢿⣿⣿⣿⣷⢿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⢿⣿⣿⣿⡿⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢯⣌⣓⣲⡾⠾⠿⣿⡿⢿⡿⣭⣭⣥⠶⣿⣿⣳⣏⣟⣿⠼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣷⣿⣿⣿⣿⣿⠿⢋⣧⣼⣿⡟⣿⢿⠋⣹⣿⡿⠛⠛⠃⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⣿⣋⣾⢿⣽⣾⣿⡷⣿⣿⣿⡈⠻⣟⡏⢻⣿⠈⢿⣻⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⢛⣟⣫⣭⣽⣃⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣾⣿⣿⣿⡿⣿⠻⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠒⠶⠿⠷⠞⠻⠿⣦⣼⣶⣍⣀⣛⣙⣉⣱⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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