⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⠤⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡤⣤⡤⣤⣤⣀⣞⣭⡶⣟⢻⡛⣟⡹⣛⠾⣽⣗⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡞⢿⡹⣍⢳⣌⢳⡱⢎⡵⢪⣝⣿⠙⠳⣮⣧⣽⣶⣷⣿⣼⣦⣏⡽⣮⣗⢤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⡛⢦⣙⢮⡱⢎⡳⣌⢧⣙⣮⣼⠟⠛⣁⣀⣀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣝⣦⠀⠀⠀ ⠀⠀⠀⠠⠀⠀⣠⠴⠒⠒⣦⣿⠳⣬⡙⢮⣜⣦⣽⣾⣷⣻⣯⣭⣷⠾⣻⣿⣙⠯⣿⣟⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣳⡄⠀ ⠀⠀⠀⠀⢀⡼⢃⣤⣿⣿⣿⣤⣻⣤⣿⠿⠟⣛⣠⣿⠀⠻⣧⣻⣿⣧⣛⣿⣿⡼⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀ ⠀⠀⠀⢠⣟⣴⣟⠳⣼⠇⠀⠉⣉⣤⣴⡞⣿⣿⣿⣿⠀⠀⠙⢿⣿⣿⢾⣿⣿⢿⣷⣿⣿⣿⣿⡟⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠁ ⠀⠀⢠⣻⣞⠳⣌⢿⡏⣀⣴⡾⢏⢧⣻⡜⣿⢻⣿⡏⠇⠀⠀⠀⠙⢿⣬⣿⣿⣄⠟⣿⣿⡟⣿⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⡟⣬⢓⣮⣿⣿⣟⣧⢚⡭⣒⣿⣿⡏⠘⣿⠀⠀⠀⠀⠀⠰⣿⢿⣿⣭⡛⠙⣿⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⡿⡜⢦⣫⣿⣿⡿⣾⢣⣏⠶⣽⣿⢿⣧⡴⣿⣶⠄⠀⠀⠀⠀⠈⣧⣽⣿⣿⡆⠘⣇⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⢿⡳⣍⣿⣿⣿⣿⣟⣿⣣⢿⡞⣿⣿⣸⠏⡵⢿⣿⣧⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⠋⢿⣿⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡱⢮⣿⣿⣿⣿⣿⡿⣷⣿⣿⣾⣿⡏⠀⢳⣾⣿⣿⡇⠀⠀⠀⠀⠀⠙⣿⠿⠟⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣜⣿⣿⣿⣿⡿⠻⠀⢻⣿⠙⣿⣿⡹⣆⠈⢿⣿⣿⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣾⣿⣿⠟⠋⠀⠀⠀⠈⢿⠳⣜⡻⢷⡈⠀⠀⠛⠋⠁⠀⠀⢀⣥⣶⣶⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠳⣄⠀⠀⠀⠀⠀⠀⠈⠛⠗⠃⠀⣠⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠤⢤⣤⣄⣀⣀⣤⠞⡉⢼⣝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⡾⢛⡯⣍⣉⠉⠄⢡⡸⡟⢸⣷⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠻⡉⠀⠀⣼⠇⠀⢇⠀⠉⠛⠛⠋⢱⣃⣈⣿⡆⠋⠙⢳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⡙⢧⠹⣄⢸⡟⠀⠀⠘⣧⠤⣤⢤⣴⡏⠀⠀⡏⡇⢀⡴⣫⠞⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢧⡌⡍⣷⣼⣷⡒⠒⠒⠒⠚⠛⠋⠛⠛⠙⠛⠚⣛⡛⢿⣞⢉⢆⣵⠻⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠻⡛⡅⢎⣹⣿⣿⢹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠇⣻⢻⣿⣾⢁⢣⢻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⡡⢛⠛⠿⣿⣿⣿⣿⠀⠀⠀⢀⡠⣔⠙⡏⣿⠚⣦⢄⠀⠀⠀⠀⣿⢹⡿⢿⣎⢆⡹⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣴⣾⣯⣯⣔⠣⡙⢄⣫⣾⣿⣿⣷⡏⠀⠀⢠⠾⢦⣼⣿⣿⣿⣶⣧⡼⢓⡆⠀⠀⣿⣼⣿⣆⣭⡷⠶⣍⠽⡇⠀⠀⠀⠀ ⠀⢠⡶⠟⡟⢛⠻⣷⣄⡈⠛⣶⠛⠿⢿⣿⡿⣿⡇⠀⠀⣞⠙⣾⣿⣿⣿⣿⡿⣿⣷⠞⣣⣀⣀⣸⣿⣿⣏⠩⢓⣦⠈⢻⣧⡀⠀⠀⠀ ⠀⣿⡧⠙⠤⢃⠬⣹⣿⠿⣦⣀⣿⢀⠘⢆⠙⠓⡇⠀⠀⢸⣉⣿⣿⣷⣿⢿⣟⣻⡭⠽⠷⠒⠛⠛⠉⠛⢻⣧⣾⠋⣀⢿⡟⢿⡀⠀⠀ ⠀⣿⣠⣹⣼⣶⣿⣿⣻⣷⢾⣿⣷⡎⢠⠏⣸⡷⠁⠀⠀⣀⣷⣾⠽⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣻⢿⡏⣼⣿⢩⣷⡀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣷⡏⣾⡟⢱⣦⣴⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠋⣿⠀ ⠀⠀⠉⠛⠻⠟⠛⠉⠉⠛⠛⠃⠀⠀⠉⠙⣿⣿⡽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢋⢿⣿⣿⣿⣷⣌⡓⢌⡧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡧⢩⣾⢿⣿⣿⣿⣿⣿⣶⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡜⣣⠇⠈⠛⠿⢿⡿⠟⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡵⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢴⣋⠶⣱⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠣⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⢢⡙⢦⡜⣌⣣⣜⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀