⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠀⠒⠲⣶⡠⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠔⠛⠉⠀⠀⠀⠀⠀⠙⠺⣿⣶⣍⣿⡿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⣶⣶⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⣎⣡⢄⠀⠀⠀⠀⠀⠀⠀⠠⣀⢈⠻⠿⣟⢲⣏⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡞⠻⠟⠘⠻⣿⣿⣿⣿⡿⠿⠟⠛⣉⡿⠿⣟⣒⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠞⡛⢫⡖⢏⡠⣠⠄⠀⠀⠀⠀⣜⡿⠷⡀⠧⣙⡞⣿⣟⢎⣟⢆⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡷⣢⡆⠰⡯⠿⣯⣿⣷⣾⣗⠊⢈⣑⠚⠻⢯⣟⡡⢿⣦⡀⠀⠀⠀⠀ ⠀⠀⢀⣎⠮⢐⡉⡴⢫⣻⢫⠆⢰⣦⠀⠀⢐⣷⣾⡙⡿⠯⠀⢾⢿⣄⠾⣿⣷⡄⠀⢀⣶⣿⢻⢹⣿⣿⠛⢹⠃⠀⠀⡸⡿⣿⣿⣿⣿⣷⣶⡛⣦⣴⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀ ⠀⢀⣾⡕⢣⣋⡴⣿⣯⣾⣿⣱⡬⢤⡇⠀⢠⣿⣿⣷⠀⠀⣊⢻⣿⠃⣷⣷⣿⡿⣦⣼⣿⣠⣼⣿⠿⢀⠀⠀⠀⠀⢠⢠⣦⣾⣿⣿⣿⣿⣿⣿⣿⣶⣝⢿⣿⡿⡿⣛⣿⣧⠀⠀ ⠀⣼⣿⣠⢿⣿⣃⣼⣿⣏⣼⢾⠋⠞⡄⡄⠈⣿⣿⣿⡄⠀⢿⢿⣿⡪⢼⣿⣥⢳⣿⣿⣿⠸⡈⠉⠀⠁⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣆⠀ ⢰⣻⣿⣟⣺⡿⣿⣿⣿⣇⣧⡋⢻⡠⣷⡇⠈⣹⣿⣿⣿⣷⡞⠋⢏⢃⠈⢿⣿⣞⢿⣿⣿⡶⡦⢤⣶⡄⠀⠠⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠻⢏⠘⡈⣿⣿⣿⣿⣿⣿⠀ ⢨⣿⣾⣿⣿⣾⣿⣟⣿⣧⣿⣷⡏⣇⠿⣿⣠⠜⣿⣿⣿⣿⣷⢀⡀⠈⢣⡄⢹⠋⡛⡟⢿⣷⣽⡿⠛⠃⠀⠆⠀⠀⣷⠛⠛⠋⠙⢹⣿⠏⣿⠃⠀⠏⣤⢆⣧⣿⣿⣿⣿⣿⣿⡇ ⠀⣿⣷⢿⣿⣿⣿⣿⣾⣿⣏⣿⣿⣿⣆⡹⠀⠀⠈⠻⣿⣿⣿⡆⠀⣀⣠⡤⣺⠀⣶⢻⣬⣽⣿⡄⢴⣾⣷⡠⢆⡾⣸⠀⠀⢀⣤⡿⠁⣸⡿⠀⠀⠀⢦⣻⣏⣿⢿⢿⠹⣿⣿⡇ ⠀⢹⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⢿⣿⣷⢲⣄⠀⣀⠙⣿⣿⣻⣆⡋⠿⠽⠟⠀⠰⡿⠯⢀⣿⣷⣤⠿⠩⢧⢼⢻⠃⠀⢀⡾⠋⠀⠼⠏⠀⠀⠀⠀⠨⣟⣦⣯⣧⣷⣶⣿⣿⣿ ⠀⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣿⣾⡍⠘⠥⠀⠛⣿⣿⣿⣿⣦⣀⣴⣦⣶⡀⢰⣾⠀⠀⠉⢣⣤⣼⡿⣿⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢫⢫⢞⣿⢹⢟⣿⣿⡟ ⠀⠸⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⠏⠉⡀⠂⠀⠨⣿⣿⣯⠈⠙⠻⣿⣿⡍⠉⢽⣿⠀⠀⠀⠀⠉⣿⣠⣧⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣹⣸⣿⣿⣞⣿⣿⠇ ⠀⠀⠘⣿⣯⣻⣾⣿⣿⣿⣷⣿⡏⣿⣯⣻⣗⡀⢈⠂⠀⣸⣿⣿⣿⣷⣦⣤⣀⠉⠙⠻⠽⠟⠀⠀⠀⠀⠀⠙⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⣖⣿⣿⣿⣿⣽⣿⡿⠀ ⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢱⣆⢣⠀⠀⡠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⣐⣡⣾⣿⣿⣟⣿⣿⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⠻⣿⣿⣾⣿⣽⣿⣟⢛⣥⣼⣯⡟⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢹⣡⣾⣽⡫⣯⣿⣿⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣗⠀⠸⣻⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⠾⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣰⣿⡷⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣏⣷⢸⣟⣿⣿⢯⠀⣀⢸⣿⣿⣿⣿⣿⣿⣄⣠⣤⣀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢞⣉⣟⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⢿⣿⣻⠳⠅⠀⠰⣾⡿⠝⣿⣿⣿⣿⠟⣻⣿⡏⢻⣷⣶⠋⠀⢀⣠⠠⣴⠒⠂⣀⣠⣶⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⡽⣿⣤⣾⠀⢀⣨⣷⣶⣵⣿⣿⠿⠋⠁⣀⡤⠚⠁⠁⣠⣴⣾⣿⣵⠖⣚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⢯⡷⢈⣽⣿⣿⡿⠋⠁⠀⠀⣾⣻⣋⡮⠞⠉⣠⠿⠛⠋⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡝⢺⣆⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣀⣀⠠⠴⠾⠿⠛⠛⠿⣿⣿⣿⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⢀⣼⣞⣵⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⣟⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢀⣴⣯⣿⣿⠟⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣦⡀⠀⢠⣞⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣤⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀