⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠛⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⡛⢼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣍⠻⣷⣦⣀⠀⠀⠀⢀⣾⣿⣿⠟⣿⣾⣿⣿⣦⣦⣠⣀⡀⢀⣴⣿⠛⢤⢃⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡰⢂⠝⡻⣷⣦⣶⡿⣿⣿⢏⡜⡰⢻⣿⣿⣯⠙⠯⣛⠻⢿⠫⡐⢍⠢⢼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠉⠶⢁⠎⣿⡏⠀⣿⣿⢆⠇⢱⢇⣾⡿⠁⠀⠀⢿⠸⢰⣿⣷⡈⠱⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣏⠜⣬⣾⣿⠀⠀⠈⠙⠚⠲⠚⠋⠁⠀⠀⠀⣀⡾⢷⣧⣿⠿⡛⢇⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⠚⡹⢛⡿⢷⣄⡀⠀⠀⠀⠀⠀⠀⣠⡴⢾⡭⣝⢺⠲⡝⣷⣵⠞⠉⠉⢿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢫⢿⡷⣷⢿⡹⢧⢯⡝⣷⣲⣤⡴⣞⡟⣧⣛⢧⡳⢎⢯⡹⣜⠲⡽⣦⣄⣀⣬⣾⣏⠹⣛⣿⢷⣷⣦⣀⡀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣎⡟⣮⢳⡝⣮⡝⣯⢞⡽⣲⢳⣎⢷⣹⣚⡥⣏⠶⣍⡏⣖⢳⡌⡟⡴⢣⢏⡽⣌⠳⣿⠟⡝⢦⡛⡴⠯⣛⠿⡿⣷⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⢷⡽⣷⢫⡞⣵⠻⣜⠯⣞⡵⣫⢞⢮⡵⢮⡱⢎⡷⣺⡜⣬⠳⣜⡱⢭⡓⢮⢲⡍⣳⡏⡏⣜⢣⡽⣙⢖⡲⢏⣵⣿⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⣵⣸⣿⣙⢮⡳⣝⢮⢻⣜⣻⣜⡳⢭⢞⡣⢞⠵⢛⡽⢳⣿⣜⡲⣙⢦⡹⢲⡙⣎⠳⣜⣿⢱⡘⢬⡓⡼⣩⢮⣵⡿⠛⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⣏⠧⡙⠤⣿⣣⢞⣱⢣⢏⡞⣣⢎⡽⣮⣝⠳⣎⠽⣭⢛⣽⡼⠟⠓⠛⠓⠭⣶⢩⢧⡹⣼⡽⠟⠹⡆⡜⢢⡙⣴⣿⠟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⢓⣁⣎⢖⡩⢒⢿⡱⣎⢎⡳⢎⡵⣍⡾⠜⠋⠉⣉⠉⠙⣶⣭⣇⡠⡤⠖⡒⠲⡄⢫⣿⢣⠳⡭⢷⡀⠀⠹⣴⣵⡿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣯⣎⣷⡘⢮⠔⣃⠚⣿⣬⢳⡙⣎⠶⣹⢤⡔⡶⢋⠡⠙⡆⢧⠒⡤⣇⣇⠘⠤⢥⡜⡿⣎⢧⢛⡼⡹⣷⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⣷⣮⣥⣝⣸⣏⢻⣾⣬⣷⣵⡟⢧⢣⣂⢔⣳⢎⣏⡜⣴⡎⠮⣝⣚⡭⢾⡗⣏⢎⡳⣜⡱⣻⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠻⢿⣿⡝⣫⢟⣻⣿⣯⡝⣢⣥⡒⠭⣘⢛⡛⢌⡒⢆⠳⣌⢻⣟⡜⢮⡱⢎⣵⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡔⣫⢦⣹⡏⡽⠁⢀⣙⡧⣆⢣⡘⣔⣸⡬⠵⠚⢻⣿⣎⢧⡙⣮⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣽⣴⣶⣿⣷⠓⢯⣿⡿⠀⠘⡆⠀⠀⠀⠀⣀⣤⣿⡿⠿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣿⣿⣿⣄⣀⠭⠧⢴⣾⣿⣿⢿⣟⡻⠽⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⡶⣆⣶⣿⠿⡉⣶⡿⠿⡆⠀⠀⢿⣿⡾⣿⣎⢹⣁⠏⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠈⢱⠿⠕⠒⢧⠕⠉⢀⣠⣵⡄⠀⠀⢻⣝⡳⡌⢧⡘⡜⡰⣙⢯⣶⣦⣀⣴⡦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣆⡀⠈⡧⠛⠉⠑⠺⢴⡱⣌⠶⠼⠝⠛⠋⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⣄⡠⠘⠛⢳⡿⣿⣿⣿⣿⣽⣿⣿⣦⣄⣀⠀⠀⠀⠀⠙⠁⠀⠀⣀⣠⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡶⣄⡂⠙⠉⠿⣇⣈⣿⣿⣿⣿⣯⠿⠿⠿⢶⠒⠒⣚⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣶⣦⣍⣽⠿⣿⣿⣉⣀⣠⣤⣤⣶⣾⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣇⣀⣽⡟⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀